Final TS Covid Project

Load Packages

library(RCurl)
library(tswge)
library(nnfor)
library(vars)
library(tidyverse)
library(lubridate)
library(tseries)
library(RColorBrewer)

Defined Functions

Bring in peak finding function

#Can also be used to find valleys if you put -x in instead of x for realization
find_peaks <- function (x, m = 3){
    shape <- diff(sign(diff(x, na.pad = FALSE)))
    pks <- sapply(which(shape < 0), FUN = function(i){
       z <- i - m + 1
       z <- ifelse(z > 0, z, 1)
       w <- i + m + 1
       w <- ifelse(w < length(x), w, length(x))
       if(all(x[c(z : i, (i + 2) : w)] <= x[i + 1])) return(i + 1) else return(numeric(0))
    })
     pks <- unlist(pks)
     pks
}

Bring in valley finding function

find_valleys <- function (x, m = 3){
    x=-x
    shape <- diff(sign(diff(x, na.pad = FALSE)))
    pks <- sapply(which(shape < 0), FUN = function(i){
       z <- i - m + 1
       z <- ifelse(z > 0, z, 1)
       w <- i + m + 1
       w <- ifelse(w < length(x), w, length(x))
       if(all(x[c(z : i, (i + 2) : w)] <= x[i + 1])) return(i + 1) else return(numeric(0))
    })
     pks <- unlist(pks)
     pks
}

Bring in rolling window ASE function

Rolling_Window_ASE = function(series, trainingSize, horizon = 1, s = 0, d = 0, phis = 0, thetas = 0)
{
ASEHolder = numeric()

for( i in 1:(length(series)-(trainingSize + horizon) + 1))
{
  
  forecasts = fore.aruma.wge(series[i:(i+(trainingSize-1))],phi = phis, theta = thetas, s = s, d = d,n.ahead = horizon)
  
  ASE = mean((series[(trainingSize+i):(trainingSize+ i + (horizon) - 1)] - forecasts$f)^2)
         
  ASEHolder[i] = ASE

}

ASEHolder
hist(ASEHolder)
WindowedASE = mean(ASEHolder)

print("The Summary Statistics for the Rolling Window ASE Are:")
print(summary(ASEHolder))
print(paste("The Rolling Window ASE is: ",WindowedASE))
return(WindowedASE)
}

Summarized EDA

Read in the data set data types

covid <- read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/merged_data.csv"))
covid$Date=mdy(covid$Date)
str(covid)

## 'data.frame':    416 obs. of  10 variables:
##  $ Date                                              : Date, format: "2020-09-14" "2020-09-15" ...
##  $ tests_taken                                       : int  34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
##  $ case_count                                        : int  3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
##  $ retail_and_recreation_percent_change_from_baseline: int  -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
##  $ grocery_and_pharmacy_percent_change_from_baseline : int  -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
##  $ parks_percent_change_from_baseline                : int  1 7 7 16 6 21 -6 -29 -28 -9 ...
##  $ transit_stations_percent_change_from_baseline     : int  -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
##  $ workplaces_percent_change_from_baseline           : int  -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
##  $ residential_percent_change_from_baseline          : int  9 10 10 10 9 3 4 12 15 12 ...
##  $ vaccine_doses_administered                        : int  0 0 0 0 0 0 0 0 0 0 ...

summary(covid)

##       Date             tests_taken       case_count   
##  Min.   :2020-09-14   Min.   :     0   Min.   :   45  
##  1st Qu.:2020-12-26   1st Qu.: 61048   1st Qu.: 2325  
##  Median :2021-04-09   Median : 92026   Median : 4661  
##  Mean   :2021-04-09   Mean   : 95723   Mean   : 6876  
##  3rd Qu.:2021-07-22   3rd Qu.:126984   3rd Qu.:10311  
##  Max.   :2021-11-03   Max.   :268222   Max.   :28027  
##  retail_and_recreation_percent_change_from_baseline
##  Min.   :-78.00                                    
##  1st Qu.:-16.00                                    
##  Median : -9.00                                    
##  Mean   :-11.65                                    
##  3rd Qu.: -6.00                                    
##  Max.   :  6.00                                    
##  grocery_and_pharmacy_percent_change_from_baseline
##  Min.   :-55.000                                  
##  1st Qu.: -9.000                                  
##  Median : -4.000                                  
##  Mean   : -4.442                                  
##  3rd Qu.:  1.000                                  
##  Max.   : 29.000                                  
##  parks_percent_change_from_baseline
##  Min.   :-76.000                   
##  1st Qu.:-16.000                   
##  Median : -3.000                   
##  Mean   : -5.724                   
##  3rd Qu.:  6.000                   
##  Max.   : 30.000                   
##  transit_stations_percent_change_from_baseline
##  Min.   :-68.00                               
##  1st Qu.:-26.00                               
##  Median :-16.00                               
##  Mean   :-18.01                               
##  3rd Qu.:-10.00                               
##  Max.   :  0.00                               
##  workplaces_percent_change_from_baseline
##  Min.   :-86.00                         
##  1st Qu.:-33.00                         
##  Median :-29.00                         
##  Mean   :-27.25                         
##  3rd Qu.:-16.75                         
##  Max.   : -7.00                         
##  residential_percent_change_from_baseline vaccine_doses_administered
##  Min.   :-1.000                           Min.   :     0            
##  1st Qu.: 5.000                           1st Qu.: 18829            
##  Median : 7.000                           Median : 63698            
##  Mean   : 7.288                           Mean   : 81305            
##  3rd Qu.: 9.000                           3rd Qu.:104878            
##  Max.   :29.000                           Max.   :374014

cases=read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/Texas%20COVID-19%20Case%20Count%20Data%20by%20County.csv"))
cases$Date=mdy(cases$Date)
cases$Case.Count=c(NA,diff(cases$Case.Count))
cases=cases[2:length(cases$Date),]
str(cases)

## 'data.frame':    611 obs. of  2 variables:
##  $ Date      : Date, format: "2020-03-05" "2020-03-06" ...
##  $ Case.Count: int  0 5 0 0 7 3 3 4 0 0 ...

Plot reduced and full data and check for consistent covariance

plotts.sample.wge(covid$case_count,lag.max = 100,trunc = 35)

## $autplt
##   [1]  1.000000000  0.742528247  0.568188353  0.568594327  0.576982271
##   [6]  0.569425145  0.701936212  0.788346677  0.670085415  0.549747319
##  [11]  0.550653544  0.541369785  0.520023441  0.613463198  0.686238834
##  [16]  0.579105471  0.475534601  0.479380813  0.450467986  0.434639425
##  [21]  0.511259716  0.571558900  0.484968510  0.387938490  0.369553508
##  [26]  0.356754837  0.330746556  0.423751392  0.490012795  0.377929103
##  [31]  0.250386855  0.234576763  0.244437559  0.230451758  0.302175735
##  [36]  0.341339575  0.244001358  0.141616768  0.129190829  0.137548097
##  [41]  0.133370112  0.190744990  0.222369375  0.138301667  0.068050640
##  [46]  0.068718459  0.042690803  0.034864433  0.088966626  0.124168606
##  [51]  0.047142091 -0.013793944 -0.005246058 -0.006333880 -0.037576153
##  [56]  0.013757960  0.048489410 -0.011703692 -0.076379088 -0.069127874
##  [61] -0.075131620 -0.088294390 -0.050668572 -0.029211398 -0.084167395
##  [66] -0.132178208 -0.135934445 -0.144845032 -0.142898050 -0.113375908
##  [71] -0.080610695 -0.123443259 -0.164019315 -0.158974635 -0.168804967
##  [76] -0.194097063 -0.161856993 -0.136231418 -0.175128917 -0.202941176
##  [81] -0.192376059 -0.192316547 -0.204487542 -0.183439209 -0.158478309
##  [86] -0.186326837 -0.233922192 -0.223170036 -0.218729881 -0.234557086
##  [91] -0.212228469 -0.183881154 -0.204548312 -0.233565249 -0.245103441
##  [96] -0.251428011 -0.258432767 -0.223506684 -0.181614570 -0.208993778
## [101] -0.242637258
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  15.3915975  18.4632526  11.2853210  11.0716564   0.3093163   4.9499390
##   [7]   2.0109647   0.4500694  -8.8568076  -7.7816920 -16.2112771  -5.1474908
##  [13]  -4.3890008  -9.3369436  -0.7862864  -3.7681382  -6.2752053 -12.3708249
##  [19]  -4.4332477 -28.0916503  -5.8310822 -15.3195884 -14.1401708 -14.6743049
##  [25] -14.9448720 -21.3642778 -38.2589161  -5.9216012  -1.8099687 -10.4638673
##  [31]  -4.4354118 -35.4157764 -14.8011192  -6.2561408  -3.8950515 -10.8533207
##  [37]  -7.6537160 -14.4593527 -11.3330937  -5.9793930  -3.5008067  -8.1084935
##  [43] -17.7647573  -7.8158450 -11.6786247  -1.7831609  -0.6907818  -5.6565398
##  [49]  -2.8314629 -13.8965331   0.2349314  -3.5370873 -10.2305864  -4.0536018
##  [55]  -5.9246423   0.9755728  -4.4226530   4.5916244   9.9584147  -2.4912398
##  [61]   7.2710740   2.5987828  -2.9453740  -1.8352426  -5.5600948 -13.3310388
##  [67]  -6.8021784  -8.5531231  -5.3218649  -7.2003684  -2.3388024   0.6952226
##  [73]  -5.8407752  -1.8277963  -1.9053610  -7.1484594  -4.7470266  -8.7136451
##  [79]  -4.4813375 -18.7421273  -6.7853728 -49.5661075 -12.8856800 -11.1383088
##  [85]  -2.0006269 -11.1693950  -5.3939753  -5.1994213 -14.8737813  -4.0758832
##  [91]  -5.5409990  -5.4659455  -5.7376952  -9.5106980  -7.0640107 -10.4334016
##  [97]  -7.7547565 -12.8322066 -13.9305763 -12.2960066 -10.0585227  -5.6928946
## [103]  -2.7778360  -2.2893742 -11.6249579  -6.9351941  -7.1960405 -14.1564481
## [109] -18.4128344  -6.3217552  -6.1256032  -6.2857096  -7.2415358  -5.3985614
## [115]  -3.9401621  -2.8056642   1.3802605  -5.3714900   7.5278018   1.8423490
## [121]  -0.3541421  -1.5330337  -8.5118989  -4.6759078  -5.5057884  -7.0399737
## [127]  -4.4531419 -13.8441388  -2.1971540 -28.0081310  -3.3873168 -10.8405235
## [133]  -7.0521061 -25.3589631  -4.5258446 -11.1463496  -8.6616418 -11.9312307
## [139] -13.7477494 -13.7026912  -5.8494544  -7.1039012 -21.2409298  -9.1678052
## [145] -16.2015037  -6.7772933 -11.4192224  -2.6917797 -10.2853156 -10.3603815
## [151]  -6.6987701 -13.2684788  -7.0554776 -11.4996202 -12.1916695  -8.7912438
## [157] -15.4502721  -6.2453446 -14.3429745 -10.4618932 -13.3261658 -16.9944583
## [163] -15.3686823 -16.7002621 -22.0137817  -4.8536474 -13.0412320  -8.9138482
## [169]  -8.2819848  -9.3758574  -7.8875518 -10.0059583 -10.8398176 -11.6710773
## [175] -12.6553806 -10.2877806  -8.8393494  -9.2518667  -7.8700539  -8.3434222
## [181]  -6.6963098  -8.7142459  -7.7126224 -15.9373668  -9.7782580  -6.9771035
## [187] -21.0147620  -9.5746777 -23.7636124  -8.6439000  -8.1495797 -19.8339974
## [193] -12.1937912  -8.6442698  -5.5039774  -7.4264241  -7.2929577  -7.1695303
## [199] -13.3734137  -9.8948865  -9.9663371  -6.7578743  -9.3868384  -9.3159440
## [205]  -5.7463010 -19.1656268  -9.8296369 -26.5219166
## 
## $dbz
##   [1]  12.02854192  11.89716070  11.67763423  11.36912898  10.97048679
##   [6]  10.48023988   9.89664107   9.21772099   8.44139215   7.56563340
##  [11]   6.58881029   5.51022385   4.33103726   3.05581103   1.69496392
##  [16]   0.26847703  -1.18920694  -2.62445923  -3.96409094  -5.12617168
##  [21]  -6.04485743  -6.69677511  -7.10646502  -7.32599226  -7.40870444
##  [26]  -7.39535728  -7.31360706  -7.18324206  -7.02096705  -6.84247427
##  [31]  -6.66217771  -6.49190641  -6.33964443  -6.20882244  -6.09820664
##  [36]  -6.00223487  -5.91164133  -5.81427995  -5.69613012  -5.54251745
##  [41]  -5.33958229  -5.07595761  -4.74446755  -4.34348765  -3.87754481
##  [46]  -3.35689330  -2.79614563  -2.21236675  -1.62315879  -1.04514249
##  [51]  -0.49300501   0.02092098   0.48668804   0.89653339   1.24457518
##  [56]   1.52649133   1.73922961   1.88077252   1.94996596   1.94641343
##  [61]   1.87043569   1.72309532   1.50628683   1.22289214   0.87699837
##  [66]   0.47416528   0.02171216  -0.47103606  -0.99264357  -1.52973935
##  [71]  -2.06762524  -2.59140742  -3.08757613  -3.54571176  -3.95979491
##  [76]  -4.32861734  -4.65509647  -4.94473669  -5.20378903  -5.43768133
##  [81]  -5.65008637  -5.84272723  -6.01580802  -6.16883191  -6.30151579
##  [86]  -6.41452308  -6.50981615  -6.59056184  -6.66066581  -6.72410772
##  [91]  -6.78427148  -6.84341945  -6.90238168  -6.96045378  -7.01544033
##  [96]  -7.06375125  -7.10046163  -7.11928515  -7.11249036  -7.07089586
## [101]  -6.98418053  -6.84176747  -6.63440393  -6.35623421  -6.00676740
## [106]  -5.59195858  -5.12388280  -4.61909183  -4.09629120  -3.57411231
## [111]  -3.06949787  -2.59684037  -2.16774526  -1.79119320  -1.47389558
## [116]  -1.22070105  -1.03497228  -0.91889625  -0.87371622  -0.89988588
## [121]  -0.99714994  -1.16455530  -1.40039523  -1.70208711  -2.06598419
## [126]  -2.48712547  -2.95893755  -3.47292132  -4.01838832  -4.58235290
## [131]  -5.14972726  -5.70397562  -6.22831845  -6.70740497  -7.12912566
## [136]  -7.48604751  -7.77599377  -8.00160298  -8.16911960  -8.28692414
## [141]  -8.36427539  -8.41050094  -8.43461916  -8.44523030  -8.45049351
## [146]  -8.45806375  -8.47493914  -8.50722845  -8.55987547  -8.63637947
## [151]  -8.73854045  -8.86624852  -9.01733543  -9.18751602  -9.37046415
## [156]  -9.55808350  -9.74103377  -9.90953972 -10.05443423 -10.16827976
## [161] -10.24632252 -10.28702316 -10.29201227 -10.26550181 -10.21335268
## [166] -10.14207025 -10.05795912  -9.96656238  -9.87240222  -9.77896619
## [171]  -9.68885285  -9.60399054  -9.52585917  -9.45566648  -9.39445187
## [176]  -9.34311029  -9.30234372  -9.27255885  -9.25373608  -9.24529770
## [181]  -9.24600371  -9.25390262  -9.26636170  -9.28019560  -9.29190153
## [186]  -9.29799210  -9.29539366  -9.28185390  -9.25628645  -9.21898106
## [191]  -9.17163047  -9.11716413  -9.05942028  -9.00271769  -8.95139712
## [196]  -8.90939240  -8.87987004  -8.86495523  -8.86554764  -8.88122495
## [201]  -8.91023472  -8.94958186  -8.99522469  -9.04239227  -9.08602372
## [206]  -9.12130513  -9.14424544  -9.15220086

plotts.sample.wge(cases$Case.Count,lag.max = 40,trunc = 35)

## $autplt
##  [1] 1.0000000 0.7812711 0.6346308 0.6347067 0.6402183 0.6331306 0.7429388
##  [8] 0.8146490 0.7112276 0.6062146 0.6092684 0.5990211 0.5802352 0.6559966
## [15] 0.7155404 0.6232571 0.5353154 0.5365204 0.5139853 0.4970087 0.5586768
## [22] 0.6081906 0.5300153 0.4461105 0.4321604 0.4212868 0.3978909 0.4724666
## [29] 0.5278958 0.4278843 0.3208573 0.3087146 0.3144161 0.2986608 0.3593858
## [36] 0.3906941 0.3057663 0.2167749 0.2066178 0.2117197 0.2038381
## 
## $freq
##   [1] 0.001636661 0.003273322 0.004909984 0.006546645 0.008183306 0.009819967
##   [7] 0.011456628 0.013093290 0.014729951 0.016366612 0.018003273 0.019639935
##  [13] 0.021276596 0.022913257 0.024549918 0.026186579 0.027823241 0.029459902
##  [19] 0.031096563 0.032733224 0.034369885 0.036006547 0.037643208 0.039279869
##  [25] 0.040916530 0.042553191 0.044189853 0.045826514 0.047463175 0.049099836
##  [31] 0.050736498 0.052373159 0.054009820 0.055646481 0.057283142 0.058919804
##  [37] 0.060556465 0.062193126 0.063829787 0.065466448 0.067103110 0.068739771
##  [43] 0.070376432 0.072013093 0.073649755 0.075286416 0.076923077 0.078559738
##  [49] 0.080196399 0.081833061 0.083469722 0.085106383 0.086743044 0.088379705
##  [55] 0.090016367 0.091653028 0.093289689 0.094926350 0.096563011 0.098199673
##  [61] 0.099836334 0.101472995 0.103109656 0.104746318 0.106382979 0.108019640
##  [67] 0.109656301 0.111292962 0.112929624 0.114566285 0.116202946 0.117839607
##  [73] 0.119476268 0.121112930 0.122749591 0.124386252 0.126022913 0.127659574
##  [79] 0.129296236 0.130932897 0.132569558 0.134206219 0.135842881 0.137479542
##  [85] 0.139116203 0.140752864 0.142389525 0.144026187 0.145662848 0.147299509
##  [91] 0.148936170 0.150572831 0.152209493 0.153846154 0.155482815 0.157119476
##  [97] 0.158756137 0.160392799 0.162029460 0.163666121 0.165302782 0.166939444
## [103] 0.168576105 0.170212766 0.171849427 0.173486088 0.175122750 0.176759411
## [109] 0.178396072 0.180032733 0.181669394 0.183306056 0.184942717 0.186579378
## [115] 0.188216039 0.189852700 0.191489362 0.193126023 0.194762684 0.196399345
## [121] 0.198036007 0.199672668 0.201309329 0.202945990 0.204582651 0.206219313
## [127] 0.207855974 0.209492635 0.211129296 0.212765957 0.214402619 0.216039280
## [133] 0.217675941 0.219312602 0.220949264 0.222585925 0.224222586 0.225859247
## [139] 0.227495908 0.229132570 0.230769231 0.232405892 0.234042553 0.235679214
## [145] 0.237315876 0.238952537 0.240589198 0.242225859 0.243862520 0.245499182
## [151] 0.247135843 0.248772504 0.250409165 0.252045827 0.253682488 0.255319149
## [157] 0.256955810 0.258592471 0.260229133 0.261865794 0.263502455 0.265139116
## [163] 0.266775777 0.268412439 0.270049100 0.271685761 0.273322422 0.274959083
## [169] 0.276595745 0.278232406 0.279869067 0.281505728 0.283142390 0.284779051
## [175] 0.286415712 0.288052373 0.289689034 0.291325696 0.292962357 0.294599018
## [181] 0.296235679 0.297872340 0.299509002 0.301145663 0.302782324 0.304418985
## [187] 0.306055646 0.307692308 0.309328969 0.310965630 0.312602291 0.314238953
## [193] 0.315875614 0.317512275 0.319148936 0.320785597 0.322422259 0.324058920
## [199] 0.325695581 0.327332242 0.328968903 0.330605565 0.332242226 0.333878887
## [205] 0.335515548 0.337152209 0.338788871 0.340425532 0.342062193 0.343698854
## [211] 0.345335516 0.346972177 0.348608838 0.350245499 0.351882160 0.353518822
## [217] 0.355155483 0.356792144 0.358428805 0.360065466 0.361702128 0.363338789
## [223] 0.364975450 0.366612111 0.368248773 0.369885434 0.371522095 0.373158756
## [229] 0.374795417 0.376432079 0.378068740 0.379705401 0.381342062 0.382978723
## [235] 0.384615385 0.386252046 0.387888707 0.389525368 0.391162029 0.392798691
## [241] 0.394435352 0.396072013 0.397708674 0.399345336 0.400981997 0.402618658
## [247] 0.404255319 0.405891980 0.407528642 0.409165303 0.410801964 0.412438625
## [253] 0.414075286 0.415711948 0.417348609 0.418985270 0.420621931 0.422258592
## [259] 0.423895254 0.425531915 0.427168576 0.428805237 0.430441899 0.432078560
## [265] 0.433715221 0.435351882 0.436988543 0.438625205 0.440261866 0.441898527
## [271] 0.443535188 0.445171849 0.446808511 0.448445172 0.450081833 0.451718494
## [277] 0.453355155 0.454991817 0.456628478 0.458265139 0.459901800 0.461538462
## [283] 0.463175123 0.464811784 0.466448445 0.468085106 0.469721768 0.471358429
## [289] 0.472995090 0.474631751 0.476268412 0.477905074 0.479541735 0.481178396
## [295] 0.482815057 0.484451718 0.486088380 0.487725041 0.489361702 0.490998363
## [301] 0.492635025 0.494271686 0.495908347 0.497545008 0.499181669
## 
## $db
##   [1]  14.62709679  17.66972280  19.44130136   8.63611551  11.81032626
##   [6]  10.58683206   0.53096424   0.33956666   5.56220004   0.50807722
##  [11]  -0.03016602  -2.54607832  -3.38349759  -9.33475042  -3.72139665
##  [16]  -9.97248906  -3.94143961  -7.70399371  -7.74273558  -8.41407286
##  [21]  -7.06834990  -2.39039445  -3.35968633  -4.61169504  -5.20210169
##  [26] -14.85683910  -5.23170793  -6.82390607 -18.79048940 -11.29676156
##  [31]  -9.26662912 -14.07080281  -7.16048983 -19.30295606 -11.97498329
##  [36] -23.54570111 -11.70061950 -19.60362530  -9.19077953  -8.73955794
##  [41]  -8.26136807 -10.42500125  -2.19652312  -7.95617140  -9.21569461
##  [46]  -6.71890817 -14.80945347  -7.97055245  -7.68579286  -6.62652719
##  [51]  -6.04794563  -6.87772196 -10.88186079  -8.90593137  -9.46881046
##  [56] -14.23880279 -12.64471994  -8.02844287  -6.20433312  -4.51686572
##  [61]  -6.18996066  -9.23724972 -12.17901052 -10.64706953  -8.62285332
##  [66] -27.10851865  -2.65380459  -3.39470522  -1.15630178  -2.22651048
##  [71] -12.63608233  -4.33530561  -6.30622899  -1.96304916  -1.66647298
##  [76] -11.98019759  -3.82421762 -10.78402139  -8.72636725  -2.81118364
##  [81]  -4.33490577  -0.83940855  -3.85023746   0.83212169   3.80590102
##  [86]  -1.53945251  10.41911230   0.03206521   6.98423165   3.11487819
##  [91]  -0.60313104   3.90391550  -9.63255559  -4.73313503 -12.77455294
##  [96]  -7.59093410 -13.13029719 -10.12099447  -7.12184145  -6.34585155
## [101]  -2.46358288 -21.12618285  -8.05932984  -1.71664425  -3.51790657
## [106]  -0.22585865  -5.98483206  -3.03063696  -3.88811320  -4.52314764
## [111]  -0.85509069  -6.68427027  -6.19412958  -7.40122679 -35.79467978
## [116]  -6.15369558 -12.28574288 -11.43307162  -7.31077480  -9.72921632
## [121]  -8.28306634 -12.27872149  -8.25189953  -9.52522379  -4.27686486
## [126] -13.29499404  -4.39471067  -8.94510381 -11.13272404  -2.89593921
## [131] -14.50906082  -5.19294714  -9.33734735  -6.36883594  -8.86449931
## [136]  -6.35835688  -6.92365564 -12.52404167  -4.05762792 -12.10583366
## [141] -11.84879029 -11.52412239 -13.06121719 -13.47502444 -17.29500101
## [146] -12.15963994 -12.98213491 -10.48199513 -11.26558060  -5.60690600
## [151]  -3.04585224  -4.50634657  -3.58506672 -10.97137959  -9.11281979
## [156]  -9.40296469  -8.43519247 -11.37893228  -9.00884007 -17.17442328
## [161]  -5.79269086 -15.18330991  -6.88904152  -8.85095359  -6.82297906
## [166]  -6.83843573  -4.23033245  -6.28156129  -6.96235543  -3.28865690
## [171]  -4.99588869   0.29200008  -2.23354195   5.81459498   5.62517223
## [176]   0.38330692   1.22509076  -2.99292728  -1.79293783  -3.53914537
## [181] -13.52961069  -4.42160445 -11.68298223  -6.03073232  -6.33964697
## [186]  -7.79206172  -4.38984254 -13.31866780  -3.96602837  -5.40521993
## [191] -20.47013392  -5.29967173  -6.09161742  -6.63061983  -8.16489147
## [196]  -8.92924276 -12.81654691  -5.57754032 -12.49596456  -8.71549833
## [201] -10.28106562 -11.71620335  -8.94452709 -15.31181754 -20.00398085
## [206] -10.28958894  -7.29216861  -6.78350613 -10.00153111 -24.32675377
## [211] -16.19765744  -7.34459659 -22.32812809  -9.39338512  -7.02077476
## [216] -11.25310975  -5.72307048  -5.28025403  -9.35587729 -12.56860630
## [221] -11.01304568  -5.61036530 -13.62952214  -8.34460152  -9.42209017
## [226] -14.47320416 -13.85342319 -14.22322404 -11.86388047 -13.26939845
## [231]  -9.33298905  -6.18024160 -17.27425279 -10.31914137 -11.02260568
## [236] -17.67425789  -7.13784421 -35.52434548 -18.89126609 -19.75915030
## [241] -15.45223599 -22.31646645  -8.80754567  -5.31653385 -15.59976761
## [246] -10.60483844  -9.82938708 -11.39793692  -5.53129018 -16.66832288
## [251]  -9.96233948  -7.92086880 -16.06172675 -12.58369718  -9.63964764
## [256] -17.95293811 -12.93808221  -7.53701667 -25.67800933 -13.07030558
## [261] -14.49934213  -3.99575794 -12.65966913  -8.03159487  -7.80131065
## [266]  -8.24366045 -12.62415663  -7.26212919  -8.93149752 -22.74945560
## [271]  -8.24041644 -16.03212532  -8.89991657 -10.78696538 -13.62288273
## [276] -10.93385321 -12.98590185 -13.73108300  -9.99356142 -14.07588377
## [281]  -8.35388422 -19.38723303 -14.46799529 -11.09829209  -9.78613322
## [286]  -9.13652598  -4.54671893 -10.17326821 -11.26769421  -5.14992861
## [291]  -9.94260634 -16.49955848 -15.02661418  -9.34631459 -12.85398952
## [296]  -7.25463929  -9.36978257  -9.54720165  -8.92047917 -12.30571824
## [301]  -8.27353007  -9.09171526  -9.60823546 -16.15189774  -8.75532180
## 
## $dbz
##   [1]  12.39311114  12.33138513  12.22838209  12.08391267  11.89771228
##   [6]  11.66944185  11.39868921  11.08497150  10.72773908  10.32638181
##  [11]   9.88023877   9.38861295   8.85079326   8.26608702   7.63386743
##  [16]   6.95364254   6.22515454   5.44852196   4.62444102   3.75446751
##  [21]   2.84140360   1.88981317   0.90667584  -0.09784864  -1.10965720
##  [26]  -2.11019580  -3.07664515  -3.98335199  -4.80487151  -5.52028369
##  [31]  -6.11740750  -6.59498805  -6.96169762  -7.23252581  -7.42440509
##  [36]  -7.55281879  -7.63013726  -7.66548865  -7.66554685  -7.63561795
##  [41]  -7.58058932  -7.50551828  -7.41581663  -7.31710948  -7.21490346
##  [46]  -7.11419965  -7.01914996  -6.93280854  -6.85699072  -6.79222796
##  [51]  -6.73779849  -6.69181420  -6.65134948  -6.61260386  -6.57109444
##  [56]  -6.52187605  -6.45978627  -6.37970978  -6.27685258  -6.14701279
##  [61]  -5.98683098  -5.79400162  -5.56742677  -5.30729660  -5.01508675
##  [66]  -4.69347129  -4.34616024  -3.97767993  -3.59312111  -3.19788165
##  [71]  -2.79742786  -2.39709199  -2.00191568  -1.61654156  -1.24514922
##  [76]  -0.89142852  -0.55858159  -0.24934484   0.03397644   0.28946705
##  [81]   0.51555890   0.71098952   0.87476388   1.00612114   1.10450696
##  [86]   1.16955170   1.20105476   1.19897516   1.16342830   1.09468898
##  [91]   0.99320083   0.85959207   0.69469769   0.49958773   0.27560114
##  [96]   0.02438406  -0.25206974  -0.55137942  -0.87074392  -1.20692192
## [101]  -1.55623393  -1.91459669  -2.27760017  -2.64063482  -2.99907083
## [106]  -3.34848181  -3.68489322  -4.00502460  -4.30648767  -4.58790411
## [111]  -4.84891862  -5.09010220  -5.31276191  -5.51869057  -5.70989722
## [116]  -5.88835743  -6.05581301  -6.21363844  -6.36277917  -6.50375733
## [121]  -6.63673361  -6.76160993  -6.87815484  -6.98613325  -7.08542266
## [126]  -7.17610122  -7.25849747  -7.33319762  -7.40101273  -7.46291348
## [131]  -7.51994405  -7.57312797  -7.62337774  -7.67141771  -7.71772577
## [136]  -7.76249603  -7.80562108  -7.84668974  -7.88499446  -7.91954171
## [141]  -7.94905916  -7.97199503  -7.98650836  -7.99045314  -7.98136491
## [146]  -7.95646363  -7.91269107  -7.84680199  -7.75552446  -7.63579356
## [151]  -7.48504572  -7.30153973  -7.08465310  -6.83509563  -6.55499206
## [156]  -6.24781178  -5.91815713  -5.57145156  -5.21358434  -4.85056705
## [161]  -4.48824318  -4.13207209  -3.78699118  -3.45734722  -3.14688174
## [166]  -2.85875410  -2.59558758  -2.35952678  -2.15229822  -1.97526862
## [171]  -1.82949760  -1.71578315  -1.63469932  -1.58662579  -1.57176977
## [176]  -1.59018051  -1.64175664  -1.72624672  -1.84324306  -1.99216892
## [181]  -2.17225912  -2.38253408  -2.62176759  -2.88844887  -3.18074003
## [186]  -3.49643120  -3.83289665  -4.18705697  -4.55535473  -4.93375244
## [191]  -5.31776373  -5.70252834  -6.08293912  -6.45382379  -6.81017413
## [196]  -7.14740389  -7.46160468  -7.74976245  -8.00989881  -8.24111302
## [201]  -8.44352025  -8.61810255  -8.76650511  -8.89081698  -8.99337142
## [206]  -9.07658974  -9.14287888  -9.19458009  -9.23395750  -9.26321091
## [211]  -9.28449751  -9.29994929  -9.31167791  -9.32176289  -9.33222348
## [216]  -9.34497700  -9.36178867  -9.38421769  -9.41356450  -9.45082278
## [221]  -9.49663901  -9.55128162  -9.61462106  -9.68612233  -9.76485130
## [226]  -9.84949643  -9.93840778 -10.02965449 -10.12110110 -10.21050171
## [231] -10.29560798 -10.37428489 -10.44462515 -10.50505163 -10.55439704
## [236] -10.59195195 -10.61747608 -10.63117259 -10.63363039 -10.62574341
## [241] -10.60861811 -10.58348059 -10.55159303 -10.51418643 -10.47241318
## [246] -10.42732030 -10.37984125 -10.33080304 -10.28094400 -10.23093763
## [251] -10.18141786 -10.13300200 -10.08630824 -10.04196567 -10.00061584
## [256]  -9.96290578  -9.92947311  -9.90092475  -9.87781067  -9.86059485
## [261]  -9.84962514  -9.84510397  -9.84706158  -9.85533349  -9.86954361
## [266]  -9.88909481  -9.91316832  -9.94073367  -9.97057058 -10.00130380
## [271] -10.03145133 -10.05948528 -10.08390315 -10.10330590 -10.11647728
## [276] -10.12245789 -10.12060685 -10.11064473 -10.09267272 -10.06716607
## [281] -10.03494219  -9.99710731  -9.95498711  -9.91004830  -9.86381781
## [286]  -9.81780566  -9.77343587  -9.73198832  -9.69455279  -9.66199543
## [291]  -9.63493696  -9.61374162  -9.59851588  -9.58911590  -9.58516318
## [296]  -9.58606799  -9.59106016  -9.59922717  -9.60955874  -9.62099711
## [301]  -9.63249135  -9.64305338  -9.65181268  -9.65806630  -9.66132047

acf(cases$Case.Count[1:(length(cases$Case.Count)/2)],lag.max = 40)
acf(cases$Case.Count[(length(cases$Case.Count)/2+1):length(cases$Case.Count)],lag.max = 40)

acf(covid$case_count[1:(length(covid$case_count)/2)],lag.max = 60)
acf(covid$case_count[(length(covid$case_count)/2+1):length(covid$case_count)],lag.max = 60)

Assume you remove seasonality first

fcases_s7=artrans.wge(cases$Case.Count,phi.tr = c(rep(0,6),1),lag.max = 30)

pcases_s7=artrans.wge(covid$case_count,phi.tr = c(rep(0,6),1),lag.max = 60)

#Dicky-Fuller Test shows d=1 does not belong in the data after adding s=7
adf.test(fcases_s7)

## Warning in adf.test(fcases_s7): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  fcases_s7
## Dickey-Fuller = -6.7219, Lag order = 8, p-value = 0.01
## alternative hypothesis: stationary

#We can see the remaining data is not white noise from the ACF
full_s7=plotts.sample.wge(fcases_s7,lag.max = 50,arlimits = T)

#Use overfit to detect any additional seasonality, none found
factor.wge(phi = c(rep(0,6),1))

## 
## Coefficients of Original polynomial:  
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1-1.0000B              1.0000               1.0000       0.0000
## 1+0.4450B+1.0000B^2   -0.2225+-0.9749i      1.0000       0.2857
## 1-1.2470B+1.0000B^2    0.6235+-0.7818i      1.0000       0.1429
## 1+1.8019B+1.0000B^2   -0.9010+-0.4339i      1.0000       0.4286
##   
## 

est.ar.wge(fcases_s7,p = 17,type = "burg")[0]

## 
## Coefficients of Original polynomial:  
## 0.3600 -0.0661 0.0457 0.0738 0.0193 0.2059 -0.5236 0.2910 -0.0138 0.0847 0.0778 -0.0011 0.1181 -0.2465 0.1050 -0.0037 0.0812 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1+1.8623B+0.8828B^2   -1.0547+-0.1425i      0.9396       0.4786
## 1-0.9279B              1.0777               0.9279       0.0000
## 1-0.7318B+0.8579B^2    0.4265+-0.9919i      0.9262       0.1854
## 1-0.2039B+0.8414B^2    0.1211+-1.0834i      0.9173       0.2323
## 1+1.2719B+0.8028B^2   -0.7922+-0.7862i      0.8960       0.3756
## 1-1.4386B+0.8012B^2    0.8977+-0.6649i      0.8951       0.1015
## 1+0.8914B+0.7636B^2   -0.5837+-0.9843i      0.8739       0.3352
## 1-1.5750B+0.7165B^2    1.0991+-0.4331i      0.8465       0.0597
## 1+0.4916B+0.3902B^2   -0.6298+-1.4717i      0.6247       0.3144
##   
## 

## named list()

#Show there is white noise remaining (p=0 so null is rejected)
ljung.wge(fcases_s7,K = 24)$pval

## Obs 0.266423 0.05373704 0.03211946 0.1132684 0.1335679 0.1335933 -0.241367 0.05224615 0.1214119 0.1352167 0.1252028 0.08708691 0.03062759 0.02477118 0.01718876 0.05536113 0.09434068 0.02828528 0.05230759 -0.02482603 -0.07102701 0.03072618 0.1080432 0.06055197

## [1] 0

ljung.wge(fcases_s7,K = 48)$pval

## Obs 0.266423 0.05373704 0.03211946 0.1132684 0.1335679 0.1335933 -0.241367 0.05224615 0.1214119 0.1352167 0.1252028 0.08708691 0.03062759 0.02477118 0.01718876 0.05536113 0.09434068 0.02828528 0.05230759 -0.02482603 -0.07102701 0.03072618 0.1080432 0.06055197 0.04611405 0.005339406 0.08050327 0.166298 0.06317725 -0.05226114 -0.05449128 -0.005420944 -0.004724705 -0.002154415 -0.05919043 -0.0311847 -0.06392585 -0.09126132 -0.0197438 0.007086993 -0.02664173 -0.0395837 -0.04490998 0.02728073 0.04205537 -0.08572992 -0.03978426 -0.04199721

## [1] 0

#Use aic5 to find remaining correlation
acf(fcases_s7,lag.max = 60)
pacf(fcases_s7,lag.max = 60)

# aic5.wge(x = fcases_s7,p = 11:20,q = 4:9,type = 'bic')
# aic5.wge(x = fcases_s7,p = 2,q = 9:14,type = 'aic')

#Models based on full data
est_fcases_s7p21q8=est.arma.wge(fcases_s7,p = 21,q=8)

## 
## Coefficients of Original polynomial:  
## -0.0230 -1.0213 -0.5401 -0.4897 -0.4550 -0.2080 -0.1938 -0.1226 -0.0104 0.1365 0.1375 0.1623 0.1617 0.1532 0.0733 0.1025 0.1675 0.0892 0.1631 0.0571 0.0339 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1-0.8434B+0.9161B^2    0.4603+-0.9379i      0.9571       0.1774
## 1-0.4874B+0.8831B^2    0.2760+-1.0277i      0.9398       0.2082
## 1-1.3847B+0.8822B^2    0.7848+-0.7194i      0.9393       0.1181
## 1-0.9178B              1.0895               0.9178       0.0000
## 1+0.4712B+0.8325B^2   -0.2830+-1.0588i      0.9124       0.2916
## 1-1.5629B+0.7633B^2    1.0238+-0.5118i      0.8737       0.0738
## 1+1.7231B+0.7609B^2   -1.1322+-0.1795i      0.8723       0.4750
## 1+1.5068B+0.7564B^2   -0.9961+-0.5744i      0.8697       0.4168
## 1+1.0733B+0.7475B^2   -0.7179+-0.9069i      0.8646       0.3566
## 1+9e-04B+0.6831B^2   -6e-04+-1.2099i      0.8265       0.2501
## 1+0.4441B+0.2770B^2   -0.8016+-1.7227i      0.5263       0.3193
##   
## 

#Run ljung test with autocrrelation
plotts.sample.wge(est_fcases_s7p21q8$res,lag.max = 40,arlimits = T)

## $autplt
##  [1]  1.000000e+00 -9.575288e-03  8.219057e-03  4.304189e-04 -9.360672e-05
##  [6]  8.497172e-03 -5.677494e-03  9.498815e-03 -1.225131e-02  8.556901e-03
## [11] -3.288750e-04 -1.108729e-02  5.068849e-03 -1.187879e-02 -2.071742e-03
## [16] -2.063961e-02  7.330368e-03 -1.551226e-02 -2.717393e-02  5.872504e-03
## [21] -5.540850e-03  1.409232e-04  5.275180e-03  2.800586e-02  1.503545e-02
## [26]  7.670708e-02  4.703620e-03  3.051079e-02  8.746116e-02  1.253057e-02
## [31] -2.237561e-02 -1.960129e-02  5.792155e-02 -4.540360e-02 -3.360992e-02
## [36] -3.756302e-02 -1.671010e-02 -2.542129e-02 -8.742100e-02 -1.373872e-02
## [41]  2.559448e-02
## 
## $freq
##   [1] 0.001655629 0.003311258 0.004966887 0.006622517 0.008278146 0.009933775
##   [7] 0.011589404 0.013245033 0.014900662 0.016556291 0.018211921 0.019867550
##  [13] 0.021523179 0.023178808 0.024834437 0.026490066 0.028145695 0.029801325
##  [19] 0.031456954 0.033112583 0.034768212 0.036423841 0.038079470 0.039735099
##  [25] 0.041390728 0.043046358 0.044701987 0.046357616 0.048013245 0.049668874
##  [31] 0.051324503 0.052980132 0.054635762 0.056291391 0.057947020 0.059602649
##  [37] 0.061258278 0.062913907 0.064569536 0.066225166 0.067880795 0.069536424
##  [43] 0.071192053 0.072847682 0.074503311 0.076158940 0.077814570 0.079470199
##  [49] 0.081125828 0.082781457 0.084437086 0.086092715 0.087748344 0.089403974
##  [55] 0.091059603 0.092715232 0.094370861 0.096026490 0.097682119 0.099337748
##  [61] 0.100993377 0.102649007 0.104304636 0.105960265 0.107615894 0.109271523
##  [67] 0.110927152 0.112582781 0.114238411 0.115894040 0.117549669 0.119205298
##  [73] 0.120860927 0.122516556 0.124172185 0.125827815 0.127483444 0.129139073
##  [79] 0.130794702 0.132450331 0.134105960 0.135761589 0.137417219 0.139072848
##  [85] 0.140728477 0.142384106 0.144039735 0.145695364 0.147350993 0.149006623
##  [91] 0.150662252 0.152317881 0.153973510 0.155629139 0.157284768 0.158940397
##  [97] 0.160596026 0.162251656 0.163907285 0.165562914 0.167218543 0.168874172
## [103] 0.170529801 0.172185430 0.173841060 0.175496689 0.177152318 0.178807947
## [109] 0.180463576 0.182119205 0.183774834 0.185430464 0.187086093 0.188741722
## [115] 0.190397351 0.192052980 0.193708609 0.195364238 0.197019868 0.198675497
## [121] 0.200331126 0.201986755 0.203642384 0.205298013 0.206953642 0.208609272
## [127] 0.210264901 0.211920530 0.213576159 0.215231788 0.216887417 0.218543046
## [133] 0.220198675 0.221854305 0.223509934 0.225165563 0.226821192 0.228476821
## [139] 0.230132450 0.231788079 0.233443709 0.235099338 0.236754967 0.238410596
## [145] 0.240066225 0.241721854 0.243377483 0.245033113 0.246688742 0.248344371
## [151] 0.250000000 0.251655629 0.253311258 0.254966887 0.256622517 0.258278146
## [157] 0.259933775 0.261589404 0.263245033 0.264900662 0.266556291 0.268211921
## [163] 0.269867550 0.271523179 0.273178808 0.274834437 0.276490066 0.278145695
## [169] 0.279801325 0.281456954 0.283112583 0.284768212 0.286423841 0.288079470
## [175] 0.289735099 0.291390728 0.293046358 0.294701987 0.296357616 0.298013245
## [181] 0.299668874 0.301324503 0.302980132 0.304635762 0.306291391 0.307947020
## [187] 0.309602649 0.311258278 0.312913907 0.314569536 0.316225166 0.317880795
## [193] 0.319536424 0.321192053 0.322847682 0.324503311 0.326158940 0.327814570
## [199] 0.329470199 0.331125828 0.332781457 0.334437086 0.336092715 0.337748344
## [205] 0.339403974 0.341059603 0.342715232 0.344370861 0.346026490 0.347682119
## [211] 0.349337748 0.350993377 0.352649007 0.354304636 0.355960265 0.357615894
## [217] 0.359271523 0.360927152 0.362582781 0.364238411 0.365894040 0.367549669
## [223] 0.369205298 0.370860927 0.372516556 0.374172185 0.375827815 0.377483444
## [229] 0.379139073 0.380794702 0.382450331 0.384105960 0.385761589 0.387417219
## [235] 0.389072848 0.390728477 0.392384106 0.394039735 0.395695364 0.397350993
## [241] 0.399006623 0.400662252 0.402317881 0.403973510 0.405629139 0.407284768
## [247] 0.408940397 0.410596026 0.412251656 0.413907285 0.415562914 0.417218543
## [253] 0.418874172 0.420529801 0.422185430 0.423841060 0.425496689 0.427152318
## [259] 0.428807947 0.430463576 0.432119205 0.433774834 0.435430464 0.437086093
## [265] 0.438741722 0.440397351 0.442052980 0.443708609 0.445364238 0.447019868
## [271] 0.448675497 0.450331126 0.451986755 0.453642384 0.455298013 0.456953642
## [277] 0.458609272 0.460264901 0.461920530 0.463576159 0.465231788 0.466887417
## [283] 0.468543046 0.470198675 0.471854305 0.473509934 0.475165563 0.476821192
## [289] 0.478476821 0.480132450 0.481788079 0.483443709 0.485099338 0.486754967
## [295] 0.488410596 0.490066225 0.491721854 0.493377483 0.495033113 0.496688742
## [301] 0.498344371 0.500000000
## 
## $db
##   [1]  -9.77929899  -1.20426742   4.35651332  -2.77132137   1.94562176
##   [6]   3.47589405  -4.32021480  -2.99824311   1.87542525   0.02702706
##  [11]  -2.06334150  -0.05913589  -6.34882872 -11.59816981  -0.01386932
##  [16] -11.22227722   1.51759371  -3.72628001  -1.14815354  -0.91395714
##  [21]   0.23023594   5.70741305   2.44972064   4.65564010  -1.42897633
##  [26]  -6.10583322   4.54359438  -0.99058832 -10.55637294   0.72086893
##  [31]  -1.44106295  -9.43304075   1.31275532 -11.39591927  -4.72922064
##  [36]  -8.71295307  -3.44390639  -2.86144499  -9.96380529   2.42379345
##  [41]  -6.86669158   3.38823179   5.41197355  -5.98767292   0.31082562
##  [46]   0.32138361  -2.34069485 -16.37172027   3.68770613  -1.88882013
##  [51]   3.36131454  -2.35326282  -0.21092350  -1.39252138  -3.31641675
##  [56]  -4.75558857  -3.88387690   2.16192708   2.67837114   2.52754457
##  [61]  -0.94126047  -4.14886550  -7.78248303  -1.16576635 -16.13089098
##  [66]  -0.31253816   3.26408439   1.53069996   3.32543501 -11.05196880
##  [71]  -0.67921511  -2.34689508   0.13545192   3.16971830 -10.15460275
##  [76]   0.34522711  -2.81384391  -4.88267002   2.81634026  -0.68477687
##  [81]   3.36388544  -2.60808725   0.78363740   0.49268402 -15.45745049
##  [86] -10.61096149 -25.59247826   1.14806125   0.56437221   0.02160886
##  [91]   6.53142546  -4.41455996   0.69549975  -4.87210214  -1.77684620
##  [96]  -3.24653658  -5.05699018  -2.52867663   1.91211209   1.47761228
## [101] -12.77945797  -1.67736090   2.41904606   0.57506859   2.53586890
## [106]  -5.33364204   0.39748867  -3.43235991   1.57257615   1.42340150
## [111]   1.12389713  -3.10860127  -0.82261667  -7.75935580   3.67466132
## [116] -14.74636008  -2.51653735   4.74740147  -7.63861288  -3.00882340
## [121]   1.61253873  -6.03672424   1.14828956   1.79007738  -2.47979190
## [126]   1.55099302 -12.37263458   2.64333310  -2.63266819   1.51616676
## [131]  -1.14402054  -1.67823563  -1.08036769   3.08557872   0.68443908
## [136]  -4.69271070   4.80508323  -0.95089634  -2.37218691  -9.42946269
## [141]  -1.02919799 -14.12046406  -4.92582155  -3.35331964  -5.67589905
## [146]  -2.43991933  -1.74767030   0.70039017   5.50639892   3.38908844
## [151]   4.95690991  -0.93006008  -1.96522604  -1.55079870  -2.28558265
## [156]  -1.28150462  -4.55144991  -4.58890598   0.88203401  -3.76075762
## [161]  -0.19775421  -2.75800538  -1.23719655  -4.20810070   2.08525015
## [166]  -0.10846805   0.12379997   2.17035256  -1.33618650   1.86003344
## [171]  -1.32375387   0.75830027  -5.91967971   1.03970388   1.65357448
## [176]  -0.57350129   1.47195129   1.17037194  -7.28359314  -0.70264530
## [181]  -6.72345573  -2.69453433  -1.68232503  -0.96826886   2.28102308
## [186] -14.05222749   4.54413215  -1.17255840  -9.15924929   3.91570087
## [191]  -1.60187836   2.37716373   2.51564053  -4.60794056  -1.62224114
## [196]   4.74426690  -6.01744204  -2.43749837   1.32386836  -3.71621110
## [201]   0.09561005  -9.94282391  -6.02172854   0.78313274   2.60344383
## [206]   2.06668691  -4.84275872 -14.85272554  -0.70422152  -1.06799506
## [211]  -6.30169864   0.98989557   0.51120159   0.35341363   4.88026431
## [216]   0.08373863  -1.18221568  -2.29930343   1.45643548   2.02181927
## [221]  -3.17608712   2.14967439 -10.60426437  -0.37748044  -4.81415248
## [226]  -8.89212484   1.60253408  -3.98948876   4.52838995  -0.50769321
## [231]   0.99824569  -6.91414267   1.16015958   3.02579936  -4.80165614
## [236]  -6.25120486  -6.55125284  -6.80760141  -7.61441607  -1.08317578
## [241]   6.02167827  -9.52141826   0.70156992   1.74330176  -5.59396822
## [246]   5.38227855  -4.92824975  -1.38845055   2.00605359  -3.51850894
## [251]  -4.54306750   1.50016400  -7.11688082  -2.30051184   2.70514710
## [256] -18.92963515  -4.22623350   5.42827996   2.32026493  -7.86315042
## [261]   0.21840996   2.10150965   2.11884594  -1.02652032   4.07876184
## [266]   1.45090777  -7.23516742   2.51235330  -9.41439635   2.92038546
## [271]  -1.79006825  -2.56083939   1.02440722  -4.97518117  -0.56585593
## [276]  -0.82251513  -1.47424713   1.17030786 -15.73910277  -3.16811046
## [281]  -0.08004264  -1.49401838   2.58714144   4.15736023  -3.36455266
## [286]   0.64515396   3.81841874  -5.57795474  -5.26282469  -3.11941199
## [291]  -1.31727081  -0.95562353   2.18359764  -1.35524703   1.07806579
## [296]  -0.16226653  -1.25407842   2.79056025  -4.11538445  -0.19271379
## [301]   1.50718118  -9.32041614
## 
## $dbz
##   [1]  0.050827449  0.032661218  0.003281459 -0.035869658 -0.082607029
##   [6] -0.133897761 -0.185811829 -0.233585390 -0.271851575 -0.295073074
##  [11] -0.298166361 -0.277242645 -0.230325145 -0.157869090 -0.062938681
##  [16]  0.049015584  0.170721945  0.293851725  0.409816486  0.510467221
##  [21]  0.588629754  0.638471990  0.655738369  0.637901943  0.584280815
##  [26]  0.496150139  0.376857646  0.231920864  0.069048556 -0.102008210
##  [31] -0.269894630 -0.422485718 -0.548136919 -0.637212666 -0.683564455
##  [36] -0.685526376 -0.646086756 -0.572173656 -0.473308412 -0.360053372
##  [41] -0.242641615 -0.130004802 -0.029234113  0.054604622  0.118417680
##  [46]  0.160895699  0.182263540  0.184008694  0.168606538  0.139247847
##  [51]  0.099569381  0.053389597  0.004456041 -0.043783804 -0.088373088
##  [56] -0.126982764 -0.157985282 -0.180462958 -0.194158496 -0.199382922
##  [61] -0.196900069 -0.187806092 -0.173418062 -0.155179333 -0.134582992
##  [66] -0.113109990 -0.092176141 -0.073082117 -0.056962360 -0.044731725
##  [71] -0.037031801 -0.034181810 -0.036141118 -0.042491589 -0.052447915
##  [76] -0.064902541 -0.078508526 -0.091798661 -0.103332737 -0.111857909
##  [81] -0.116461356 -0.116691789 -0.112628363 -0.104882626 -0.094529916
##  [86] -0.082978553 -0.071795168 -0.062510393 -0.056430347 -0.054476550
##  [91] -0.057071906 -0.064084499 -0.074835134 -0.088168784 -0.102583953
##  [96] -0.116407250 -0.127993485 -0.135925757 -0.139187330 -0.137279465
## [101] -0.130267458 -0.118749613 -0.103757756 -0.086609361 -0.068737677
## [106] -0.051526445 -0.036170790 -0.023578007 -0.014313367 -0.008588617
## [111] -0.006285527 -0.007003836 -0.010122375 -0.014863592 -0.020354766
## [116] -0.025683212 -0.029946850 -0.032304593 -0.032032082 -0.028586851
## [121] -0.021682888 -0.011368767  0.001902444  0.017227520  0.033248478
## [126]  0.048202486  0.060032930  0.066559650  0.065698068  0.055710639
## [131]  0.035469861  0.004709243 -0.035764683 -0.083931154 -0.136522818
## [136] -0.189144394 -0.236579915 -0.273304457 -0.294171993 -0.295189466
## [141] -0.274229421 -0.231512013 -0.169726117 -0.093753084 -0.010065916
## [146]  0.074048414  0.151282443  0.214996437  0.259742700  0.281622072
## [151]  0.278500063  0.250116919  0.198114904  0.125985329  0.038915086
## [156] -0.056504662 -0.152747199 -0.242013757 -0.317057790 -0.372064635
## [161] -0.403418128 -0.410170323 -0.394087472 -0.359260580 -0.311390021
## [166] -0.256924735 -0.202234492 -0.152937264 -0.113431571 -0.086627159
## [171] -0.073838857 -0.074804444 -0.087797906 -0.109824412 -0.136895307
## [176] -0.164385154 -0.187465750 -0.201594369 -0.203009842 -0.189169873
## [181] -0.159057254 -0.113298974 -0.054078589  0.015133616  0.089972655
## [186]  0.165618222  0.237213947  0.300221092  0.350687227  0.385431727
## [191]  0.402162812  0.399545320  0.377236606  0.335902325  0.277216177
## [196]  0.203839249  0.119366325  0.028219900 -0.064530327 -0.153440995
## [201] -0.233066836 -0.298412194 -0.345413732 -0.371378860 -0.375294147
## [206] -0.357934009 -0.321741420 -0.270505114 -0.208901291 -0.141987198
## [211] -0.074726424 -0.011600580  0.043667770  0.088280174  0.120428846
## [216]  0.139283414  0.144915927  0.138179271  0.120551686  0.093959263
## [221]  0.060589516  0.022711227 -0.017482644 -0.057993023 -0.097082196
## [226] -0.133287204 -0.165386008 -0.192333504 -0.213191636 -0.227079817
## [231] -0.233167622 -0.230721499 -0.219203122 -0.198401772 -0.168570782
## [236] -0.130532309 -0.085717846 -0.036123756  0.015821634  0.067465296
## [241]  0.116184093  0.159653809  0.196100558  0.224507350  0.244754457
## [246]  0.257676947  0.265026330  0.269327321  0.273628027  0.281154881
## [251]  0.294902446  0.317209124  0.349385189  0.391460678  0.442102449
## [256]  0.498715551  0.557704943  0.614843753  0.665682652  0.705942114
## [261]  0.731848519  0.740396933  0.729540778  0.698318243  0.646927042
## [266]  0.576754930  0.490365458  0.391429360  0.284584342  0.175203300
## [271]  0.069056761 -0.028127344 -0.111175307 -0.175986649 -0.219972198
## [276] -0.242321377 -0.244037626 -0.227733128 -0.197230136 -0.157054397
## [281] -0.111914725 -0.066244849 -0.023852496  0.012309884  0.040259773
## [286]  0.059002076  0.068468861  0.069398449  0.063167854  0.051591145
## [291]  0.036697421  0.020505189  0.004813472 -0.008968230 -0.019930997
## [296] -0.027705002 -0.032422319 -0.034612734 -0.035051676 -0.034585855
## [301] -0.033963872 -0.033696276

acf(est_fcases_s7p21q8$res,lag.max = 50)
pacf(est_fcases_s7p21q8$res,lag.max = 60)
ljung.wge(x = est_fcases_s7p21q8$res,K = 24,p = 2,q = 8)

## Obs -0.009575288 0.008219057 0.0004304189 -9.360672e-05 0.008497172 -0.005677494 0.009498815 -0.01225131 0.008556901 -0.000328875 -0.01108729 0.005068849 -0.01187879 -0.002071742 -0.02063961 0.007330368 -0.01551226 -0.02717393 0.005872504 -0.00554085 0.0001409232 0.00527518 0.02800586 0.01503545

## $test
## [1] "Ljung-Box test"
## 
## $K
## [1] 24
## 
## $chi.square
## [1] 2.139682
## 
## $df
## [1] 14
## 
## $pval
## [1] 0.9998743

ljung.wge(x = est_fcases_s7p21q8$res,K = 48,p = 2,q = 8)

## Obs -0.009575288 0.008219057 0.0004304189 -9.360672e-05 0.008497172 -0.005677494 0.009498815 -0.01225131 0.008556901 -0.000328875 -0.01108729 0.005068849 -0.01187879 -0.002071742 -0.02063961 0.007330368 -0.01551226 -0.02717393 0.005872504 -0.00554085 0.0001409232 0.00527518 0.02800586 0.01503545 0.07670708 0.00470362 0.03051079 0.08746116 0.01253057 -0.02237561 -0.01960129 0.05792155 -0.0454036 -0.03360992 -0.03756302 -0.0167101 -0.02542129 -0.087421 -0.01373872 0.02559448 -0.01264854 -0.01854353 -0.0665434 0.02314855 0.05067647 -0.05989914 0.02035279 -0.01398838

## $test
## [1] "Ljung-Box test"
## 
## $K
## [1] 48
## 
## $chi.square
## [1] 31.18086
## 
## $df
## [1] 38
## 
## $pval
## [1] 0.775425

#Identify Rolling Window ASE for short term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 7,s = 7,phis = est_fcases_s7p21q8$phi,thetas = est_fcases_s7p21q8$theta,trainingSize = 60)

#Identify Rolling Window ASE for long term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 21,s = 7,phis = est_fcases_s7p21q8$phi,thetas = est_fcases_s7p21q8$theta,trainingSize = 60)

Assume it has no seasonality

fcases_d1=artrans.wge(covid$case_count,phi.tr = c(1),lag.max = 40)

pcases_d1=artrans.wge(cases$Case.Count,phi.tr = c(1),lag.max = 40)

#Dicky-Fuller Test shows another d=1 does not belong in the data
adf.test(fcases_d1)

## Warning in adf.test(fcases_d1): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  fcases_d1
## Dickey-Fuller = -11.526, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary

#We can see the remaining data is not white noise from the ACF
full_s7=plotts.sample.wge(fcases_d1,lag.max = 50,arlimits = T)

#Use overfit to detect any additional seasonality, none found
factor.wge(phi = c(rep(0,2),1))

## 
## Coefficients of Original polynomial:  
## 0.0000 0.0000 1.0000 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1+1.0000B+1.0000B^2   -0.5000+-0.8660i      1.0000       0.3333
## 1-1.0000B              1.0000               1.0000       0.0000
##   
## 

est.ar.wge(fcases_d1,p = 17,type = "burg")[0]

## 
## Coefficients of Original polynomial:  
## -0.5836 -0.7007 -0.6390 -0.5329 -0.5513 -0.2735 0.0220 0.0778 0.0780 0.1346 0.1723 0.1007 0.1063 0.2291 0.1611 0.0851 0.1106 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1-1.2009B+0.9274B^2    0.6474+-0.8118i      0.9630       0.1429
## 1+0.4521B+0.9201B^2   -0.2457+-1.0132i      0.9592       0.2879
## 1+1.0939B+0.8069B^2   -0.6779+-0.8831i      0.8983       0.3542
## 1-0.8904B              1.1231               0.8904       0.0000
## 1+1.5313B+0.7718B^2   -0.9920+-0.5582i      0.8785       0.4184
## 1+1.7121B+0.7537B^2   -1.1358+-0.1916i      0.8682       0.4734
## 1-1.4665B+0.7446B^2    0.9848+-0.6109i      0.8629       0.0884
## 1-0.5548B+0.7039B^2    0.3941+-1.1249i      0.8390       0.1964
## 1-0.0933B+0.5918B^2    0.0788+-1.2975i      0.7693       0.2403
##   
## 

## named list()

#Show there is white noise remaining (p=0 so null is rejected)
ljung.wge(fcases_d1,K = 24)$pval

## Obs -0.1615376 -0.3407416 -0.01630825 0.03173191 -0.272202 0.08906849 0.4012604 0.007109842 -0.2423124 0.02006031 0.0242998 -0.2228805 0.03869155 0.3513558 -0.006603022 -0.2096946 0.06250296 -0.0239695 -0.1784947 0.03014485 0.2871098 0.02060267 -0.155077 -0.01105907

## [1] 0

ljung.wge(fcases_d1,K = 48)$pval

## Obs -0.1615376 -0.3407416 -0.01630825 0.03173191 -0.272202 0.08906849 0.4012604 0.007109842 -0.2423124 0.02006031 0.0242998 -0.2228805 0.03869155 0.3513558 -0.006603022 -0.2096946 0.06250296 -0.0239695 -0.1784947 0.03014485 0.2871098 0.02060267 -0.155077 -0.01105907 0.02673451 -0.2309074 0.05145384 0.3487136 0.02987283 -0.2194925 -0.04987516 0.04801155 -0.1662238 0.06290646 0.2665929 0.01054959 -0.1774367 -0.0401461 0.02638368 -0.1197962 0.04881206 0.2276451 -0.02742431 -0.1410507 0.05162234 -0.0320819 -0.1193104 0.03610111

## [1] 0

#Use aic5 to find remaining correlation
acf(fcases_d1,lag.max = 60)
pacf(fcases_d1,lag.max = 60)

#aic5.wge(x = fcases_d1,p = 25:30,q = 10:15,type = 'aic')

#Models based on full data
est_fcases_d1p6q14=est.arma.wge(fcases_d1,p = 6,q=14)

## 
## Coefficients of Original polynomial:  
## -0.8997 -0.8878 -0.9762 -0.8031 -0.9918 -0.7810 
## 
## Factor                 Roots                Abs Recip    System Freq 
## 1-1.2331B+0.9808B^2    0.6286+-0.7902i      0.9904       0.1431
## 1+0.4399B+0.9769B^2   -0.2252+-0.9864i      0.9884       0.2857
## 1+1.6928B+0.8152B^2   -1.0383+-0.3855i      0.9029       0.4434
##   
## 

#Run ljung test with autocrrelation
plotts.sample.wge(est_fcases_d1p6q14$res,lag.max = 40,arlimits = T)

## $autplt
##  [1]  1.0000000000  0.0013083094 -0.0008560196 -0.0007060941 -0.0001362948
##  [6]  0.0006523680 -0.0046918922  0.0045626103  0.0016006571 -0.0098654627
## [11] -0.0187965302  0.0210342051 -0.0112466654  0.0150252014  0.0125231684
## [16] -0.0061664781  0.0179894403  0.0684617345 -0.0353518445  0.0231186747
## [21] -0.0127348803 -0.0473077082  0.0222093115  0.0701347085  0.0229771437
## [26]  0.0588875602 -0.0122746166  0.0729060111  0.1249720762  0.0497055270
## [31] -0.0364885749 -0.0832642272  0.0285201266 -0.0194777219 -0.0037059795
## [36] -0.0343991007 -0.0362657349 -0.0440623114 -0.1093781267 -0.0163020552
## [41]  0.0332095800
## 
## $freq
##   [1] 0.002409639 0.004819277 0.007228916 0.009638554 0.012048193 0.014457831
##   [7] 0.016867470 0.019277108 0.021686747 0.024096386 0.026506024 0.028915663
##  [13] 0.031325301 0.033734940 0.036144578 0.038554217 0.040963855 0.043373494
##  [19] 0.045783133 0.048192771 0.050602410 0.053012048 0.055421687 0.057831325
##  [25] 0.060240964 0.062650602 0.065060241 0.067469880 0.069879518 0.072289157
##  [31] 0.074698795 0.077108434 0.079518072 0.081927711 0.084337349 0.086746988
##  [37] 0.089156627 0.091566265 0.093975904 0.096385542 0.098795181 0.101204819
##  [43] 0.103614458 0.106024096 0.108433735 0.110843373 0.113253012 0.115662651
##  [49] 0.118072289 0.120481928 0.122891566 0.125301205 0.127710843 0.130120482
##  [55] 0.132530120 0.134939759 0.137349398 0.139759036 0.142168675 0.144578313
##  [61] 0.146987952 0.149397590 0.151807229 0.154216867 0.156626506 0.159036145
##  [67] 0.161445783 0.163855422 0.166265060 0.168674699 0.171084337 0.173493976
##  [73] 0.175903614 0.178313253 0.180722892 0.183132530 0.185542169 0.187951807
##  [79] 0.190361446 0.192771084 0.195180723 0.197590361 0.200000000 0.202409639
##  [85] 0.204819277 0.207228916 0.209638554 0.212048193 0.214457831 0.216867470
##  [91] 0.219277108 0.221686747 0.224096386 0.226506024 0.228915663 0.231325301
##  [97] 0.233734940 0.236144578 0.238554217 0.240963855 0.243373494 0.245783133
## [103] 0.248192771 0.250602410 0.253012048 0.255421687 0.257831325 0.260240964
## [109] 0.262650602 0.265060241 0.267469880 0.269879518 0.272289157 0.274698795
## [115] 0.277108434 0.279518072 0.281927711 0.284337349 0.286746988 0.289156627
## [121] 0.291566265 0.293975904 0.296385542 0.298795181 0.301204819 0.303614458
## [127] 0.306024096 0.308433735 0.310843373 0.313253012 0.315662651 0.318072289
## [133] 0.320481928 0.322891566 0.325301205 0.327710843 0.330120482 0.332530120
## [139] 0.334939759 0.337349398 0.339759036 0.342168675 0.344578313 0.346987952
## [145] 0.349397590 0.351807229 0.354216867 0.356626506 0.359036145 0.361445783
## [151] 0.363855422 0.366265060 0.368674699 0.371084337 0.373493976 0.375903614
## [157] 0.378313253 0.380722892 0.383132530 0.385542169 0.387951807 0.390361446
## [163] 0.392771084 0.395180723 0.397590361 0.400000000 0.402409639 0.404819277
## [169] 0.407228916 0.409638554 0.412048193 0.414457831 0.416867470 0.419277108
## [175] 0.421686747 0.424096386 0.426506024 0.428915663 0.431325301 0.433734940
## [181] 0.436144578 0.438554217 0.440963855 0.443373494 0.445783133 0.448192771
## [187] 0.450602410 0.453012048 0.455421687 0.457831325 0.460240964 0.462650602
## [193] 0.465060241 0.467469880 0.469879518 0.472289157 0.474698795 0.477108434
## [199] 0.479518072 0.481927711 0.484337349 0.486746988 0.489156627 0.491566265
## [205] 0.493975904 0.496385542 0.498795181
## 
## $db
##   [1]  -5.979200749   4.853218808   1.730262672   2.458077251  -6.537585992
##   [6]   1.335814543  -1.357039730  -1.683463469  -6.834339701  -6.291968971
##  [11] -14.563072409  -3.729585234  -0.673962095  -3.538504014   4.737728994
##  [16]   2.635246097   1.970765879  -5.900146427   4.179737593 -12.133748523
##  [21]   2.576546182  -6.375369255  -3.811442484  -4.306877625  -7.352313154
##  [26] -14.203698823 -19.441249042   2.524421031   7.512491118  -6.888343576
##  [31]   3.314402083 -16.173119179  -8.322717194   0.890566311   3.863824819
##  [36]  -5.341585084  -0.805469198  -9.101966087  -6.364534637   0.881163819
##  [41]   2.352306347  -5.721072681 -25.713951416  -4.252666029  -4.519706222
##  [46]   3.056979511   4.740959892  -5.688988308   2.221313400  -3.143611479
##  [51]   2.400212525  -0.374154956  -5.405087608   1.225570924  -4.405360152
##  [56]   1.771600146   0.040771587  -3.074854601   1.582413830  -5.767742753
##  [61]   2.490427471   3.470899716  -7.658136035  -0.779672194  -1.635976876
##  [66]  -6.007745612  -2.325197083  -0.559304982  -5.323170707  -1.180273286
##  [71]   1.117471470   5.626365758  -0.306094627   1.888039401   4.485690891
##  [76]  -2.885055208  -2.381270067  -7.993699428   0.997303122  -7.893325326
##  [81]  -0.255793106  -9.001316904  -6.070418449  -7.384868406   3.614028514
##  [86]  -0.279278934  -1.547772169   3.964184632  -7.486166384  -0.778412250
##  [91]   0.452006658   2.191858951   1.504092849   2.620409573  -5.369877309
##  [96] -10.423209358  -2.369090781  -4.330658880  -4.199163399  -3.701520540
## [101]  -2.793191720   4.650358921   3.510252280   3.661293962  -2.645778785
## [106]  -0.786899261  -0.017565062  -1.730780514  -2.674854092  -5.579651405
## [111]   0.495287367  -1.404912475   1.943316573   0.002537396   1.147719616
## [116]  -3.528004901   1.534873992  -0.181935698  -2.988733834   0.858486913
## [121]  -2.427774594   4.086243096  -2.814760790  -3.654800859  -0.032245263
## [126]  -1.412806505   4.186599472  -3.880488314   2.224390869  -3.097296969
## [131]   1.456941334   1.623262811  -0.129285398  -0.788489430  -3.678372355
## [136]  -3.667104211  -2.912035882  -1.696235169  -9.461752189  -1.866744217
## [141]   2.319676497  -1.117456269 -11.832258526   1.305206178  -3.795018056
## [146]   1.674775087   1.412355673   4.253674911   0.259852595  -2.731847387
## [151]   4.207346228   2.106721876  -5.902584380  -3.280940605  -8.568020078
## [156]   1.251159482   3.928859062  -3.409267169  -2.106785533  -2.255258274
## [161]   1.356061574 -10.325024422 -12.758670089  -3.772921485   2.231770549
## [166]   0.456644976   2.539031253  -7.992554192   5.118370383 -16.796537063
## [171]   2.771559825 -10.966145056   1.029308125 -10.186852742   1.181352550
## [176] -22.059652657  -1.810194707   4.084812937  -4.773580705   1.302227997
## [181]  -5.449041399   3.621791193  -1.987497736   2.537307391  -9.295322137
## [186]   0.341511740  -1.493332887  -0.525931599   0.172385941  -1.962447249
## [191]   1.395873608  -8.708466376   1.130073932  -0.868513141   4.719440804
## [196]  -1.499833757   4.096922897  -6.873271384  -4.499052026  -1.520680810
## [201]   2.592660780  -2.530107474   0.889731020  -1.252411949  -0.505980352
## [206]  -2.863325161  -2.029537135
## 
## $dbz
##   [1]  0.3790383552  0.3176212211  0.2216434478  0.1005050465 -0.0331937083
##   [6] -0.1646393315 -0.2784983776 -0.3612538707 -0.4037265051 -0.4029835769
##  [11] -0.3628693412 -0.2928997180 -0.2059526835 -0.1155832751 -0.0337066105
##  [16]  0.0309785921  0.0737998990  0.0942911078  0.0958759464  0.0851154364
##  [21]  0.0705275468  0.0610212581  0.0641189871  0.0843136054  0.1219956755
##  [26]  0.1732813361  0.2307829414  0.2850503557  0.3262508629  0.3457058914
##  [31]  0.3370769233  0.2971628466  0.2263591503  0.1288264964  0.0123528745
##  [36] -0.1121842532 -0.2318853032 -0.3334860831 -0.4054565032 -0.4400976371
##  [41] -0.4349984087 -0.3933210493 -0.3228145117 -0.2339555834 -0.1378723306
##  [46] -0.0446139238  0.0379535141  0.1046134040  0.1527619336  0.1820363887
##  [51]  0.1937553568  0.1902873454  0.1744454204  0.1489955848  0.1163531384
##  [56]  0.0785125110  0.0372093480 -0.0057429539 -0.0480521970 -0.0866257128
##  [61] -0.1174775807 -0.1359829529 -0.1375215080 -0.1184320066 -0.0770631669
##  [66] -0.0146133355  0.0645297868  0.1530898763  0.2417717703  0.3204652149
##  [71]  0.3795067064  0.4107954903  0.4086756386  0.3705869616  0.2975184297
##  [76]  0.1942665766  0.0694247106 -0.0650611287 -0.1949793348 -0.3057105090
##  [81] -0.3847071568 -0.4240348292 -0.4221205007 -0.3839885910 -0.3198631196
##  [86] -0.2426978770 -0.1655052514 -0.0991804138 -0.0511186959 -0.0246013729
##  [91] -0.0187974319 -0.0292497052 -0.0487809044 -0.0687823009 -0.0807901055
##  [96] -0.0781235986 -0.0572318365 -0.0183838860  0.0344974912  0.0947791705
## [101]  0.1545190836  0.2059304406  0.2426008388  0.2603161939  0.2574717244
## [106]  0.2351177313  0.1966976472  0.1475235761  0.0940323394  0.0428901065
## [111]  0.0000618988 -0.0299925573 -0.0448301180 -0.0441349519 -0.0294311964
## [116] -0.0035143886  0.0302147045  0.0683338142  0.1077795084  0.1459835976
## [121]  0.1807965670  0.2102761521  0.2324388693  0.2450675816  0.2456447690
## [126]  0.2314471136  0.1998019794  0.1484790325  0.0761746252 -0.0169600100
## [131] -0.1288015466 -0.2548184857 -0.3878177619 -0.5180179225 -0.6336201483
## [136] -0.7220104711 -0.7715687547 -0.7737820761 -0.7250822761 -0.6277655433
## [141] -0.4896407647 -0.3225642422 -0.1404247005  0.0427875987  0.2144161515
## [146]  0.3639691147  0.4834497729  0.5673704515  0.6126210371  0.6183121450
## [151]  0.5856576320  0.5179136152  0.4203508432  0.3002004163  0.1664796120
## [156]  0.0295843368 -0.0994517139 -0.2100584121 -0.2934785700 -0.3440857927
## [161] -0.3602909250 -0.3447191546 -0.3035706077 -0.2453594688 -0.1794021726
## [166] -0.1144212265 -0.0574984468 -0.0134546971  0.0153731166  0.0290277601
## [171]  0.0295686312  0.0205073065  0.0061011128 -0.0094137186 -0.0225361478
## [176] -0.0310304884 -0.0341600905 -0.0325739519 -0.0278827045 -0.0220386016
## [181] -0.0166751446 -0.0125588415 -0.0092707457 -0.0051862641  0.0022320705
## [186]  0.0158718543  0.0382419320  0.0707339577  0.1130525413  0.1629609927
## [191]  0.2164061630  0.2679805601  0.3115979106  0.3412304348  0.3515817252
## [196]  0.3386232541  0.2999758906  0.2351520422  0.1456846811  0.0351608912
## [201] -0.0908429272 -0.2249515436 -0.3583537766 -0.4813869276 -0.5843641877
## [206] -0.6586009627 -0.6975037276

acf(est_fcases_d1p6q14$res,lag.max = 60)
pacf(est_fcases_d1p6q14$res,lag.max = 60)
ljung.wge(x = est_fcases_d1p6q14$res,K = 24,p = 2,q = 8)

## Obs 0.001308309 -0.0008560196 -0.0007060941 -0.0001362948 0.000652368 -0.004691892 0.00456261 0.001600657 -0.009865463 -0.01879653 0.02103421 -0.01124667 0.0150252 0.01252317 -0.006166478 0.01798944 0.06846173 -0.03535184 0.02311867 -0.01273488 -0.04730771 0.02220931 0.07013471 0.02297714

## $test
## [1] "Ljung-Box test"
## 
## $K
## [1] 24
## 
## $chi.square
## [1] 7.271369
## 
## $df
## [1] 14
## 
## $pval
## [1] 0.9237437

ljung.wge(x = est_fcases_d1p6q14$res,K = 48,p = 2,q = 8)

## Obs 0.001308309 -0.0008560196 -0.0007060941 -0.0001362948 0.000652368 -0.004691892 0.00456261 0.001600657 -0.009865463 -0.01879653 0.02103421 -0.01124667 0.0150252 0.01252317 -0.006166478 0.01798944 0.06846173 -0.03535184 0.02311867 -0.01273488 -0.04730771 0.02220931 0.07013471 0.02297714 0.05888756 -0.01227462 0.07290601 0.1249721 0.04970553 -0.03648857 -0.08326423 0.02852013 -0.01947772 -0.00370598 -0.0343991 -0.03626573 -0.04406231 -0.1093781 -0.01630206 0.03320958 0.0008057241 -0.01015381 -0.03459925 0.04074889 0.05823959 -0.06546526 0.0008528935 -0.01853162

## $test
## [1] "Ljung-Box test"
## 
## $K
## [1] 48
## 
## $chi.square
## [1] 36.89734
## 
## $df
## [1] 38
## 
## $pval
## [1] 0.5203278

#Identify Rolling Window ASE for short term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 7,d = 1,phis = est_fcases_d1p6q14$phi,thetas = est_fcases_d1p6q14$theta,trainingSize = 60)

#Identify Rolling Window ASE for long term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 21,d = 1,phis = est_fcases_d1p6q14$phi,thetas = est_fcases_d1p6q14$theta,trainingSize = 60)

Generate examples from models selected

#Original Realization
plotts.wge(cases$Case.Count)

#Generated ARIMA(21,0,8)
plotts.wge(gen.aruma.wge(600,phi = est_fcases_s7p21q8$phi,theta =  est_fcases_s7p21q8$theta,s = 7,vara = est_fcases_s7p21q8$avar,sn = 25300))

#Generated ARIMA(6,1,14)
plotts.wge(gen.aruma.wge(600,phi = est_fcases_d1p6q14$phi,theta =  est_fcases_d1p6q14$theta,d = 1,vara = est_fcases_d1p6q14$avar,sn = 60))

Start Part 2 of Analysis

Read in the data set

covid <- read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/merged_data.csv"))
covid$Date=mdy(covid$Date)
str(covid)

## 'data.frame':    416 obs. of  10 variables:
##  $ Date                                              : Date, format: "2020-09-14" "2020-09-15" ...
##  $ tests_taken                                       : int  34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
##  $ case_count                                        : int  3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
##  $ retail_and_recreation_percent_change_from_baseline: int  -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
##  $ grocery_and_pharmacy_percent_change_from_baseline : int  -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
##  $ parks_percent_change_from_baseline                : int  1 7 7 16 6 21 -6 -29 -28 -9 ...
##  $ transit_stations_percent_change_from_baseline     : int  -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
##  $ workplaces_percent_change_from_baseline           : int  -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
##  $ residential_percent_change_from_baseline          : int  9 10 10 10 9 3 4 12 15 12 ...
##  $ vaccine_doses_administered                        : int  0 0 0 0 0 0 0 0 0 0 ...

summary(covid)

##       Date             tests_taken       case_count   
##  Min.   :2020-09-14   Min.   :     0   Min.   :   45  
##  1st Qu.:2020-12-26   1st Qu.: 61048   1st Qu.: 2325  
##  Median :2021-04-09   Median : 92026   Median : 4661  
##  Mean   :2021-04-09   Mean   : 95723   Mean   : 6876  
##  3rd Qu.:2021-07-22   3rd Qu.:126984   3rd Qu.:10311  
##  Max.   :2021-11-03   Max.   :268222   Max.   :28027  
##  retail_and_recreation_percent_change_from_baseline
##  Min.   :-78.00                                    
##  1st Qu.:-16.00                                    
##  Median : -9.00                                    
##  Mean   :-11.65                                    
##  3rd Qu.: -6.00                                    
##  Max.   :  6.00                                    
##  grocery_and_pharmacy_percent_change_from_baseline
##  Min.   :-55.000                                  
##  1st Qu.: -9.000                                  
##  Median : -4.000                                  
##  Mean   : -4.442                                  
##  3rd Qu.:  1.000                                  
##  Max.   : 29.000                                  
##  parks_percent_change_from_baseline
##  Min.   :-76.000                   
##  1st Qu.:-16.000                   
##  Median : -3.000                   
##  Mean   : -5.724                   
##  3rd Qu.:  6.000                   
##  Max.   : 30.000                   
##  transit_stations_percent_change_from_baseline
##  Min.   :-68.00                               
##  1st Qu.:-26.00                               
##  Median :-16.00                               
##  Mean   :-18.01                               
##  3rd Qu.:-10.00                               
##  Max.   :  0.00                               
##  workplaces_percent_change_from_baseline
##  Min.   :-86.00                         
##  1st Qu.:-33.00                         
##  Median :-29.00                         
##  Mean   :-27.25                         
##  3rd Qu.:-16.75                         
##  Max.   : -7.00                         
##  residential_percent_change_from_baseline vaccine_doses_administered
##  Min.   :-1.000                           Min.   :     0            
##  1st Qu.: 5.000                           1st Qu.: 18829            
##  Median : 7.000                           Median : 63698            
##  Mean   : 7.288                           Mean   : 81305            
##  3rd Qu.: 9.000                           3rd Qu.:104878            
##  Max.   :29.000                           Max.   :374014

Visualize full data and create mean mobility

str(covid)

## 'data.frame':    416 obs. of  10 variables:
##  $ Date                                              : Date, format: "2020-09-14" "2020-09-15" ...
##  $ tests_taken                                       : int  34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
##  $ case_count                                        : int  3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
##  $ retail_and_recreation_percent_change_from_baseline: int  -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
##  $ grocery_and_pharmacy_percent_change_from_baseline : int  -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
##  $ parks_percent_change_from_baseline                : int  1 7 7 16 6 21 -6 -29 -28 -9 ...
##  $ transit_stations_percent_change_from_baseline     : int  -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
##  $ workplaces_percent_change_from_baseline           : int  -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
##  $ residential_percent_change_from_baseline          : int  9 10 10 10 9 3 4 12 15 12 ...
##  $ vaccine_doses_administered                        : int  0 0 0 0 0 0 0 0 0 0 ...

names(covid)

##  [1] "Date"                                              
##  [2] "tests_taken"                                       
##  [3] "case_count"                                        
##  [4] "retail_and_recreation_percent_change_from_baseline"
##  [5] "grocery_and_pharmacy_percent_change_from_baseline" 
##  [6] "parks_percent_change_from_baseline"                
##  [7] "transit_stations_percent_change_from_baseline"     
##  [8] "workplaces_percent_change_from_baseline"           
##  [9] "residential_percent_change_from_baseline"          
## [10] "vaccine_doses_administered"

covid$mobility_mean=rowMeans(x = covid[,c(4:9)],dims = 1)
plotts.sample.wge(covid$case_count)

## $autplt
##  [1] 1.0000000 0.7425282 0.5681884 0.5685943 0.5769823 0.5694251 0.7019362
##  [8] 0.7883467 0.6700854 0.5497473 0.5506535 0.5413698 0.5200234 0.6134632
## [15] 0.6862388 0.5791055 0.4755346 0.4793808 0.4504680 0.4346394 0.5112597
## [22] 0.5715589 0.4849685 0.3879385 0.3695535 0.3567548
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  15.3915975  18.4632526  11.2853210  11.0716564   0.3093163   4.9499390
##   [7]   2.0109647   0.4500694  -8.8568076  -7.7816920 -16.2112771  -5.1474908
##  [13]  -4.3890008  -9.3369436  -0.7862864  -3.7681382  -6.2752053 -12.3708249
##  [19]  -4.4332477 -28.0916503  -5.8310822 -15.3195884 -14.1401708 -14.6743049
##  [25] -14.9448720 -21.3642778 -38.2589161  -5.9216012  -1.8099687 -10.4638673
##  [31]  -4.4354118 -35.4157764 -14.8011192  -6.2561408  -3.8950515 -10.8533207
##  [37]  -7.6537160 -14.4593527 -11.3330937  -5.9793930  -3.5008067  -8.1084935
##  [43] -17.7647573  -7.8158450 -11.6786247  -1.7831609  -0.6907818  -5.6565398
##  [49]  -2.8314629 -13.8965331   0.2349314  -3.5370873 -10.2305864  -4.0536018
##  [55]  -5.9246423   0.9755728  -4.4226530   4.5916244   9.9584147  -2.4912398
##  [61]   7.2710740   2.5987828  -2.9453740  -1.8352426  -5.5600948 -13.3310388
##  [67]  -6.8021784  -8.5531231  -5.3218649  -7.2003684  -2.3388024   0.6952226
##  [73]  -5.8407752  -1.8277963  -1.9053610  -7.1484594  -4.7470266  -8.7136451
##  [79]  -4.4813375 -18.7421273  -6.7853728 -49.5661075 -12.8856800 -11.1383088
##  [85]  -2.0006269 -11.1693950  -5.3939753  -5.1994213 -14.8737813  -4.0758832
##  [91]  -5.5409990  -5.4659455  -5.7376952  -9.5106980  -7.0640107 -10.4334016
##  [97]  -7.7547565 -12.8322066 -13.9305763 -12.2960066 -10.0585227  -5.6928946
## [103]  -2.7778360  -2.2893742 -11.6249579  -6.9351941  -7.1960405 -14.1564481
## [109] -18.4128344  -6.3217552  -6.1256032  -6.2857096  -7.2415358  -5.3985614
## [115]  -3.9401621  -2.8056642   1.3802605  -5.3714900   7.5278018   1.8423490
## [121]  -0.3541421  -1.5330337  -8.5118989  -4.6759078  -5.5057884  -7.0399737
## [127]  -4.4531419 -13.8441388  -2.1971540 -28.0081310  -3.3873168 -10.8405235
## [133]  -7.0521061 -25.3589631  -4.5258446 -11.1463496  -8.6616418 -11.9312307
## [139] -13.7477494 -13.7026912  -5.8494544  -7.1039012 -21.2409298  -9.1678052
## [145] -16.2015037  -6.7772933 -11.4192224  -2.6917797 -10.2853156 -10.3603815
## [151]  -6.6987701 -13.2684788  -7.0554776 -11.4996202 -12.1916695  -8.7912438
## [157] -15.4502721  -6.2453446 -14.3429745 -10.4618932 -13.3261658 -16.9944583
## [163] -15.3686823 -16.7002621 -22.0137817  -4.8536474 -13.0412320  -8.9138482
## [169]  -8.2819848  -9.3758574  -7.8875518 -10.0059583 -10.8398176 -11.6710773
## [175] -12.6553806 -10.2877806  -8.8393494  -9.2518667  -7.8700539  -8.3434222
## [181]  -6.6963098  -8.7142459  -7.7126224 -15.9373668  -9.7782580  -6.9771035
## [187] -21.0147620  -9.5746777 -23.7636124  -8.6439000  -8.1495797 -19.8339974
## [193] -12.1937912  -8.6442698  -5.5039774  -7.4264241  -7.2929577  -7.1695303
## [199] -13.3734137  -9.8948865  -9.9663371  -6.7578743  -9.3868384  -9.3159440
## [205]  -5.7463010 -19.1656268  -9.8296369 -26.5219166
## 
## $dbz
##   [1]  12.4980077  12.3324653  12.0557333  11.6665816  11.1633183  10.5438391
##   [7]   9.8057220   8.9464053   7.9635137   6.8554399   5.6223686   4.2680384
##  [13]   2.8026737   1.2475644  -0.3586597  -1.9537974  -3.4516289  -4.7566327
##  [19]  -5.7962290  -6.5503790  -7.0498263  -7.3459993  -7.4838913  -7.4956093
##  [25]  -7.4077784  -7.2493723  -7.0530868  -6.8513006  -6.6708737  -6.5297292
##  [31]  -6.4357567  -6.3873328  -6.3747405  -6.3822076  -6.3905846  -6.3806134
##  [37]  -6.3363081  -6.2474794  -6.1103980  -5.9262599  -5.6981243  -5.4276590
##  [43]  -5.1130146  -4.7486616  -4.3273562  -3.8436396  -3.2975421  -2.6968775
##  [49]  -2.0571084  -1.3990141  -0.7453869  -0.1180843   0.4638469   0.9849289
##  [55]   1.4332221   1.7998843   2.0786064   2.2650905   2.3566492   2.3519568
##  [61]   2.2509630   2.0549750   1.7669213   1.3918021   0.9373249   0.4146668
##  [67]  -0.1607973  -0.7691366  -1.3864194  -1.9867846  -2.5462595  -3.0475669
##  [73]  -3.4840212  -3.8604197  -4.1902335  -4.4904028  -4.7759700  -5.0562217
##  [79]  -5.3329251  -5.6005718  -5.8483686  -6.0636397  -6.2359643  -6.3608552
##  [85]  -6.4416220  -6.4887007  -6.5168890  -6.5417560  -6.5764715  -6.6297058
##  [91]  -6.7046655  -6.7990719  -6.9059014  -7.0148031  -7.1141041  -7.1931283
##  [97]  -7.2442694  -7.2640858  -7.2528728  -7.2127036  -7.1445322  -7.0453261
## [103]  -6.9062862  -6.7131285  -6.4490586  -6.1001549  -5.6613788  -5.1403628
## [109]  -4.5569225  -3.9387394  -3.3156990  -2.7153320  -2.1603810  -1.6682148
## [115]  -1.2513294  -0.9182672  -0.6745496  -0.5234461  -0.4665275  -0.5040090
## [121]  -0.6349050  -0.8570171  -1.1667695  -1.5589060  -2.0260693  -2.5583137
## [127]  -3.1426552  -3.7628456  -4.3996397  -5.0318428  -5.6382680  -6.2003292
## [133]  -6.7044889  -7.1435403  -7.5161021  -7.8246069  -8.0728340  -8.2641631
## [139]  -8.4011989  -8.4866729  -8.5249411  -8.5232053  -8.4918205  -8.4435692
## [145]  -8.3922539  -8.3511538  -8.3317754  -8.3430752  -8.3911199  -8.4790423
## [151]  -8.6071408  -8.7730075  -8.9716288  -9.1954579  -9.4345256  -9.6767136
## [157]  -9.9083545 -10.1153105 -10.2845552 -10.4060473 -10.4744165 -10.4898737
## [163] -10.4579583 -10.3881786 -10.2920209 -10.1809443 -10.0648276  -9.9510667
## [169]  -9.8442975  -9.7466123  -9.6581158  -9.5776785  -9.5037532  -9.4351221
## [175]  -9.3714511  -9.3135529  -9.2633203  -9.2233584  -9.1964047  -9.1846540
## [181]  -9.1891078  -9.2090465  -9.2417097  -9.2822576  -9.3240820  -9.3595077
## [187]  -9.3808573  -9.3817344  -9.3582555  -9.3098959  -9.2396910  -9.1537329
## [193]  -9.0601371  -8.9677863  -8.8851550  -8.8194028  -8.7757911  -8.7573878
## [199]  -8.7649820  -8.7971427  -8.8503766  -8.9193782  -8.9973873  -9.0766829
## [205]  -9.1492319  -9.2074753  -9.2451806  -9.2582295

plotts.sample.wge(covid$tests_taken)

## $autplt
##  [1] 1.0000000 0.4389657 0.3875677 0.3685486 0.4752392 0.4390029 0.4628439
##  [8] 0.4584686 0.3807932 0.4338508 0.4118061 0.4242590 0.3479843 0.3591513
## [15] 0.3587381 0.3882476 0.3662274 0.3509530 0.2916578 0.2922313 0.3578795
## [22] 0.2864460 0.3168696 0.2423636 0.2888662 0.2181025
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  11.301482768  16.742501527  13.938286669   7.504777383  -0.400126316
##   [6]   2.391341544   1.073663371  -6.857810339   1.678387751   0.638385980
##  [11]  -6.182935039  -3.469259133  -8.723612579  -5.426715232  -1.316160648
##  [16]   0.797637990  -5.618760155  -4.127587274  -5.988584416  -6.058339606
##  [21]  -7.695388765  -2.578776800  -6.820386550  -5.576576412  -4.508218184
##  [26] -13.876321507  -3.174791842 -16.732836142  -8.768701185  -3.577321043
##  [31]  -1.202154668  -5.038512028  -8.331710704  -4.066469401  -4.852897903
##  [36]  -1.371009223 -34.283467220 -23.779467922  -3.737088080  -5.812902916
##  [41]  -9.218636437  -0.579846142  -2.748092277  -4.390244359  -3.393223261
##  [46]  -0.292061649  -4.534397018 -13.770173502   2.405587355   1.210473331
##  [51]  -9.150274921  -6.865624284  -3.297440451 -18.989750087  -2.442401237
##  [56]  -1.786787712  -2.646506136  -6.608748724   5.333370671  -0.722509695
##  [61]  -8.721982527  -3.067603641  -3.913130547  -3.547350197  -5.991583655
##  [66]  -4.681809451 -14.114927540  -3.176836413  -6.360535874  -0.499462294
##  [71]   0.183307045  -2.082160462   1.075049473   0.245116747  -1.768675373
##  [76]  -6.056625760  -1.316002484  -1.477120281  -3.920164578   6.793413599
##  [81]   0.004314842  -6.645020575  -4.919219669  -4.324277485   2.828021178
##  [86]  -0.333430600  -5.642506320  -1.400377926  -8.215132811   3.392776823
##  [91]  -7.785385949  -7.275891232  -1.546634350 -11.759421968  -8.578455264
##  [96]  -1.761168880   0.224506803  -0.150603128 -13.705803799  -6.619692601
## [101]  -0.596506069  -4.898663361  -0.293108454  -7.217629556   2.214680664
## [106]  -9.300503349  -6.359843900   2.975161673  -2.168245042  -1.949975193
## [111]  -3.882536088 -10.949097544  -3.060185856  -1.729569711 -23.959001796
## [116]  -4.613753882  -2.769643394  -5.111552083   3.235249654   3.528232631
## [121] -14.236526706  -9.861521007  -6.653801570  -3.123817336 -10.751069548
## [126]   4.104365745  -1.474074947  -8.692513432  -1.517413116  -2.083189487
## [131]   0.282553039 -10.578790204  -7.968846007  -2.603150864  -0.476766421
## [136]  -4.945883435  -4.335297028  -5.880510375  -7.728565405 -13.622615583
## [141]  -0.171147878 -22.837692732   1.495014077  -1.966990856  -6.072698146
## [146]  -4.768052086  -8.848059167  -0.633937164  -6.348319911  -5.897781046
## [151]  -4.651051143  -5.826110039 -10.083918946  -7.864396637   1.435736442
## [156]  -6.297410926 -11.668116458  -7.582812623 -11.741405252 -17.414356795
## [161]  -6.281131357  -2.370400417 -15.243980620  -4.976417827  -7.941595279
## [166] -25.342125839  -2.477548401  -3.832264481  -6.854448428  -1.104286257
## [171]   0.485117435 -10.624120674  -8.815420092   0.172519564  -7.578435629
## [176]  -5.189221838   0.280241668  -3.674721947  -5.618911571  -6.132505319
## [181]  -4.317429733  -2.250085356  -7.044884748  -5.489149712   0.846110509
## [186]   1.359802470  -8.750868858  -3.966329245 -13.613887995   4.972532577
## [191]   1.267481407   3.533672260  -7.928548779  -6.868175544  -2.893487925
## [196]  -4.748188636  -3.529268289  -9.334279299  -7.733091735  -4.448188504
## [201]  -0.827648576  -0.715687584  -3.219041616  -3.081507901  -5.250788983
## [206]  -8.063543780   0.924605929  -5.903270635
## 
## $dbz
##   [1] 10.87672478 10.71859138 10.45463892 10.08433601  9.60708180  9.02238869
##   [7]  8.33018305  7.53129055  6.62820635  5.62629016  4.53555023  3.37312416
##  [13]  2.16627394  0.95493760 -0.20848654 -1.26552826 -2.16572145 -2.88308098
##  [19] -3.42359762 -3.81738281 -4.10208744 -4.30931762 -4.45957058 -4.56402637
##  [25] -4.62915472 -4.66090982 -4.66687606 -4.65616767 -4.63784998 -4.61895889
##  [31] -4.60296306 -4.58908966 -4.57260281 -4.54594354 -4.50052089 -4.42879948
##  [37] -4.32618289 -4.19216716 -4.03043960 -3.84797039 -3.65348495 -3.45582873
##  [43] -3.26262881 -3.07944538 -2.90942677 -2.75339021 -2.61023030 -2.47756562
##  [49] -2.35253458 -2.23263418 -2.11647000 -2.00427749 -1.89810530 -1.80162141
##  [55] -1.71958724 -1.65710876 -1.61879294 -1.60791698 -1.62567926 -1.67057326
##  [61] -1.73792860 -1.81970207 -1.90466212 -1.97915400 -2.02858997 -2.03961124
##  [67] -2.00252518 -1.91330322 -1.77440775 -1.59413283 -1.38477090 -1.16033522
##  [73] -0.93455160 -0.71951046 -0.52502001 -0.35849319 -0.22514942 -0.12834916
##  [79] -0.06994325 -0.05057415 -0.06990398 -0.12676585 -0.21924574 -0.34470657
##  [85] -0.49976734 -0.68025129 -0.88111896 -1.09640762 -1.31920775 -1.54172000
##  [91] -1.75544841 -1.95158789 -2.12164280 -2.25825706 -2.35614756 -2.41294241
##  [97] -2.42968652 -2.41083330 -2.36368533 -2.29741177 -2.22187343 -2.14648911
## [103] -2.07930321 -2.02631974 -1.99109865 -1.97458267 -1.97513109 -1.98876179
## [109] -2.00962422 -2.03072358 -2.04487538 -2.04579130 -2.02910943 -1.99313570
## [115] -1.93910578 -1.87090911 -1.79437999 -1.71637370 -1.64386220 -1.58321752
## [121] -1.53975382 -1.51751584 -1.51925406 -1.54651180 -1.59975567 -1.67849595
## [127] -1.78136323 -1.90612737 -2.04966671 -2.20791730 -2.37585393 -2.54757059
## [133] -2.71653116 -2.87603890 -3.01991894 -3.14332534 -3.24350159 -3.32028500
## [139] -3.37618920 -3.41602001 -3.44612422 -3.47346862 -3.50476093 -3.54576713
## [145] -3.60089623 -3.67304974 -3.76368627 -3.87302927 -4.00033657 -4.14414884
## [151] -4.30243843 -4.47259417 -4.65120761 -4.83367514 -5.01369963 -5.18286044
## [157] -5.33050734 -5.44427938 -5.51147918 -5.52126555 -5.46718580 -5.34917855
## [163] -5.17419051 -4.95509901 -4.70838906 -4.45146914 -4.20040613 -3.96843732
## [169] -3.76522174 -3.59659671 -3.46459057 -3.36752466 -3.30014774 -3.25385643
## [175] -3.21714884 -3.17651120 -3.11789816 -3.02878341 -2.90044067 -2.72981695
## [181] -2.52032676 -2.28125367 -2.02601231 -1.76992531 -1.52818493 -1.31439096
## [187] -1.13972936 -1.01264896 -0.93882943 -0.92126024 -0.96030884 -1.05371664
## [193] -1.19651450 -1.38090366 -1.59620792 -1.82906803 -2.06409401 -2.28516088
## [199] -2.47736140 -2.62930742 -2.73513211 -2.79545047 -2.81685913 -2.81015260
## [205] -2.78790558 -2.76214139 -2.74254009 -2.73529822

plotts.sample.wge(covid$vaccine_doses_administered)

## $autplt
##  [1] 1.0000000 0.8739978 0.7176945 0.6405640 0.6291265 0.6764781 0.8038319
##  [8] 0.8976695 0.7846137 0.6382382 0.5697411 0.5636810 0.6139153 0.7380781
## [15] 0.8303145 0.7249350 0.5914640 0.5304595 0.5250483 0.5719471 0.6935498
## [22] 0.7827134 0.6756766 0.5425374 0.4836029 0.4823595
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  19.8031590  16.5776853   8.4412122   2.2692821  -3.7506238   4.6644615
##   [7] -11.8620479 -11.8394877  -7.3771724  -8.5171703  -4.6411310   2.2644852
##  [13]  -2.6237705   3.0870535  -4.0197681   1.4603474  -2.2313672 -16.2964445
##  [19]  -4.0429167  -5.8135809  -3.6026858 -10.1835512 -18.3845286  -7.9079386
##  [25]  -4.2292645  -8.7632611  -2.4807396  -6.8808953  -2.9822247  -8.9408405
##  [31]  -9.3893926 -22.1984069 -27.7860778 -17.4879359 -21.6218563 -11.5544712
##  [37]  -7.3506140  -8.2727532 -23.7231678 -16.0248719 -17.6932012 -24.9912830
##  [43] -13.6342967  -5.1161024  -4.1625455  -3.7397838 -12.0454814 -15.1932008
##  [49] -24.2456263 -19.3442044 -26.6466035 -17.6847422  -9.9609037  -5.6279883
##  [55]  -3.8905548  -7.9359161  -0.1804803   5.2430989  10.8429959  10.0398269
##  [61]   3.7482925   1.2430409  -6.2126859  -4.2137135  -8.4144517 -13.0738966
##  [67] -15.9059014 -27.8219245 -14.7036111 -11.7152205 -13.7819145 -10.0760627
##  [73]  -9.4334624 -14.5706632 -10.0971016 -13.4075679  -7.5545256 -21.9267874
##  [79] -17.9699735 -33.0857903 -22.7334698 -28.1449051 -15.8630842 -22.0528487
##  [85] -10.1148729 -16.1206581 -17.7191448 -21.7006892 -28.8189877 -22.7341323
##  [91] -28.8041913 -18.5658677 -20.4065001 -16.7679390 -14.6314233 -15.4111069
##  [97] -22.7344409 -15.7265477 -11.2430690 -12.1876173 -13.4147465 -15.6656922
## [103] -11.5672267 -17.3503463 -17.4477962 -11.9631222 -15.6377206 -17.4345442
## [109] -30.5379090 -38.5652278 -11.0609262 -24.2002231 -11.4564842 -16.3469576
## [115] -19.9062603 -11.1256667  -3.5377852   0.2047136   5.9883934  -3.8936478
## [121]  -4.3097116 -40.9866320 -22.9485197 -22.3026175 -19.5211635 -20.5095509
## [127] -18.2959585 -17.8264900 -24.5978152 -24.5249461 -19.4589624 -15.7950286
## [133] -21.6006903 -24.0674711 -17.6157609 -16.5770373 -20.4492716 -35.7070911
## [139] -19.8255067 -16.3578606 -16.3343163 -17.3467215 -50.4725287 -20.0842116
## [145] -21.7248943 -18.8423050 -27.4947222 -15.9169183 -20.4016861 -19.5675077
## [151] -17.7157665 -21.6261069 -19.0791114 -18.9175678 -25.9022328 -15.3688348
## [157] -21.7648147 -24.8539248 -28.0186543 -26.4770252 -15.7006530 -22.7703689
## [163] -24.1471094 -32.6621384 -32.4220683 -14.0896990 -23.9027656 -21.7035386
## [169] -17.5936864 -28.1614025 -22.6763194 -23.6764886 -28.5357625 -14.0264419
## [175] -27.8796759 -14.6932928  -9.4918853  -2.6032371  -3.5233444 -16.7626445
## [181] -14.1350310 -12.2590569  -9.2160757 -22.4641841 -16.5823658 -24.8758840
## [187] -31.4532246 -21.6759018 -23.0952986 -20.2193044 -14.0913243 -27.5939366
## [193] -26.3169394 -26.1495841 -39.5512932 -16.8872991 -14.5149737 -16.0831032
## [199] -12.5278486 -23.8445423 -23.1621474 -24.1838867 -20.9260170 -21.7691310
## [205] -16.7109886 -17.3245034 -15.7383890 -27.5638586
## 
## $dbz
##   [1]  13.1746181  12.9955964  12.6963481  12.2756110  11.7317517  11.0629552
##   [7]  10.2675690   9.3447123   8.2953394   7.1240462   5.8420217   4.4715035
##  [13]   3.0514794   1.6423237   0.3231856  -0.8260467  -1.7566566  -2.4744796
##  [19]  -3.0310044  -3.4902959  -3.9001045  -4.2813949  -4.6327468  -4.9421118
##  [25]  -5.2000988  -5.4097165  -5.5888271  -5.7653950  -5.9693546  -6.2252509
##  [31]  -6.5474260  -6.9373525  -7.3821968  -7.8545417  -8.3146178  -8.7171903
##  [37]  -9.0234694  -9.2133289  -9.2891690  -9.2666807  -9.1572646  -8.9521241
##  [43]  -8.6169908  -8.1036120  -7.3771054  -6.4431602  -5.3523257  -4.1788348
##  [49]  -2.9945020  -1.8544365  -0.7950997   0.1617934   1.0044324   1.7270440
##  [55]   2.3272703   2.8045226   3.1589897   3.3910521   3.5009381   3.4885243
##  [61]   3.3532212   3.0939126   2.7089380   2.1961214   1.5528716   0.7764017
##  [67]  -0.1358298  -1.1852841  -2.3708000  -3.6858448  -5.1138641  -6.6212086
##  [73]  -8.1487191  -9.6079236 -10.8948302 -11.9300720 -12.7028789 -13.2734210
##  [79] -13.7291471 -14.1391271 -14.5349160 -14.9134011 -15.2500593 -15.5162598
##  [85] -15.6955635 -15.7923533 -15.8288799 -15.8341523 -15.8322489 -15.8352223
##  [91] -15.8415113 -15.8387672 -15.8098423 -15.7404125 -15.6257223 -15.4735058
##  [97] -15.3016267 -15.1315840 -14.9804039 -14.8527280 -14.7336828 -14.5835592
## [103] -14.3384969 -13.9248767 -13.2900478 -12.4327790 -11.4062556 -10.2911019
## [109]  -9.1643255  -8.0836303  -7.0861791  -6.1934918  -5.4169219  -4.7618147
## [115]  -4.2302274  -3.8225896  -3.5386817  -3.3782014  -3.3410893  -3.4277126
## [121]  -3.6389635  -3.9762964  -4.4417078  -5.0376359  -5.7667279  -6.6313643
## [127]  -7.6327372  -8.7691161 -10.0326838 -11.4040565 -12.8437677 -14.2820619
## [133] -15.6149092 -16.7233431 -17.5250727 -18.0233629 -18.2981235 -18.4493071
## [139] -18.5510563 -18.6399358 -18.7236094 -18.7946903 -18.8430125 -18.8638733
## [145] -18.8612200 -18.8462063 -18.8330734 -18.8347626 -18.8598476 -18.9112270
## [151] -18.9863252 -19.0783711 -19.1783691 -19.2773627 -19.3684691 -19.4480598
## [157] -19.5155321 -19.5714358 -19.6141259 -19.6355079 -19.6169057 -19.5269484
## [163] -19.3244819 -18.9691870 -18.4380388 -17.7384076 -16.9077627 -16.0003687
## [169] -15.0712354 -14.1659806 -13.3178804 -12.5492148 -11.8740208 -11.3007245
## [175] -10.8341602 -10.4769666 -10.2304948 -10.0953701 -10.0718106 -10.1597663
## [181] -10.3589072 -10.6684547 -11.0868150 -11.6109367 -12.2352659 -12.9501371
## [187] -13.7394610 -14.5777896 -15.4275036 -16.2381982 -16.9517688 -17.5157635
## [193] -17.9013415 -18.1143869 -18.1905525 -18.1783925 -18.1229192 -18.0570290
## [199] -18.0002487 -17.9612170 -17.9411325 -17.9368849 -17.9434826 -17.9557328
## [205] -17.9692353 -17.9807956 -17.9884143 -17.9910577

plotts.sample.wge(covid$retail_and_recreation_percent_change_from_baseline)

## $autplt
##  [1] 1.0000000 0.6983174 0.5868280 0.5095025 0.4666940 0.4459558 0.4622844
##  [8] 0.4912353 0.4217998 0.3916000 0.3759614 0.3762750 0.4004297 0.4046370
## [15] 0.4153277 0.3814206 0.3774123 0.3610891 0.3448507 0.3479561 0.3513856
## [22] 0.3808831 0.3743044 0.3414351 0.3215593 0.3175316
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  18.37283971   9.36706876   7.70415501   9.35121559   1.90413861
##   [6]   7.70726735  -6.54338792   3.49863057   6.18353052   2.49014183
##  [11]   4.40450490   3.26856751  -6.31916458   2.06941390  -0.25851934
##  [16]   2.19179334   4.79782479   3.01483806   2.15211045   2.03574805
##  [21]  -3.22581164   2.45973555  -0.86087505   1.87118628   2.11256564
##  [26]   4.23767975  -4.52401881  -9.57609423  -7.32316519  -0.71563805
##  [31]  -0.60870599   3.07167438   2.42417546  -0.05708961   1.68808336
##  [36]  -0.23261918  -2.31254842  -6.58152518  -5.58007894  -0.68518727
##  [41]  -0.66766507  -1.54214733  -9.35312630  -6.61307420   0.93739896
##  [46]   1.91075212   0.19060731  -1.22771314  -2.47997926 -10.03670141
##  [51]  -9.09376483  -9.80336785  -7.33657542  -0.68898736  -0.06300741
##  [56]   2.55559683   2.51345338  -4.12752465   4.94568994  -4.34038974
##  [61]   1.91026473  -2.29485579   1.66133597  -3.42661775  -6.13934835
##  [66] -14.52807439  -2.76231778  -3.09359386  -8.13631626   0.92042640
##  [71]  -0.81184856  -0.91218853  -2.52286869  -0.48613201  -3.05808270
##  [76]  -3.98702150 -13.64096000  -4.11549841  -5.38316220 -12.37720862
##  [81]  -7.04232288 -11.35809615  -3.31756162  -3.10906774  -7.31097981
##  [86] -13.40219560  -4.58793738  -5.91688253 -10.65056319 -17.56659826
##  [91]  -5.27916952 -16.32582910  -4.20330572  -4.86005978  -7.13138023
##  [96]  -9.72321835  -4.13561362  -5.38828436  -5.81459257  -2.52326138
## [101]  -3.57376100  -5.92333027  -3.62016034  -3.42778763  -3.48482886
## [106]  -7.66275532 -13.38190272 -12.90081369  -9.63946529 -13.25402736
## [111] -11.66476282  -4.85875464  -0.92637276  -0.72684937  -5.26932552
## [116]  -7.24116777 -20.36857727   0.56805373   0.48607391  -3.93769670
## [121] -10.50132257 -10.16264005 -11.51912545 -10.58277120  -9.40788437
## [126]  -8.59176370  -5.43688229  -2.74837328   0.06498268   0.18200760
## [131]  -2.79411721  -7.83604702  -9.38332993 -22.96634701 -27.30847892
## [136] -17.81641101 -13.01545761  -2.56400034  -4.80416686  -5.80148130
## [141]  -7.37652914  -9.07906915  -6.52134671  -6.03449469  -5.50832430
## [146]  -3.84292231  -7.54405424  -7.14347196  -8.39252762  -9.92597198
## [151] -10.50410120 -13.05320945 -16.67966754  -6.33725683  -3.51609523
## [156] -15.60404613  -6.75550373  -4.95296889  -4.28758353  -7.20350796
## [161]  -2.95879620 -10.88165318  -8.47075545 -23.01099535  -9.66002295
## [166] -17.40753639 -18.30570661  -9.70160702 -19.41804135  -4.00117919
## [171]  -3.42241452  -3.44485668  -5.55612827  -0.40570966  -3.06585908
## [176]  -3.97499607  -2.69554910 -11.59661505 -10.38409343 -14.52519458
## [181] -10.01753091  -8.14674164  -3.38508893  -3.39898129  -3.06382905
## [186]  -3.52903079  -2.50098926  -4.92390430  -9.07116809  -8.46876508
## [191] -11.45289725 -17.55253463  -9.32017821 -10.98104665 -13.55311306
## [196]  -5.36245765  -5.21677875 -11.71467812  -5.57847859  -2.45550505
## [201]  -4.62797576  -9.45211666  -6.42201399  -5.16389493  -5.63762207
## [206]  -7.24831446 -10.76509440 -45.55631953
## 
## $dbz
##   [1] 11.38914925 11.23202239 10.97089913 10.60715179 10.14321876  9.58320714
##   [7]  8.93378112  8.20538523  7.41376995  6.58156536  5.73921528  4.92401004
##  [13]  4.17574146  3.52864323  3.00217907  2.59577658  2.29114556  2.06064970
##  [19]  1.87659552  1.71735102  1.56939468  1.42645132  1.28722900  1.15287173
##  [25]  1.02480185  0.90331273  0.78702336  0.67308247  0.55784770  0.43771551
##  [31]  0.30983747  0.17257660  0.02567206 -0.12984223 -0.29188371 -0.45764506
##  [37] -0.62391894 -0.78736419 -0.94467461 -1.09263241 -1.22805118 -1.34763703
##  [43] -1.44782383 -1.52466477 -1.57388231 -1.59117250 -1.57281188 -1.51651444
##  [49] -1.42235849 -1.29350750 -1.13645848 -0.96068892 -0.77777735 -0.60023395
##  [55] -0.44031897 -0.30905529 -0.21552222 -0.16641636 -0.16581329 -0.21505883
##  [61] -0.31274569 -0.45477471 -0.63454701 -0.84337128 -1.07117882 -1.30759303
##  [67] -1.54328403 -1.77137695 -1.98855265 -2.19548630 -2.39645269 -2.59820631
##  [73] -2.80846320 -3.03436295 -3.28119112 -3.55149221 -3.84459135 -4.15650061
##  [79] -4.48019399 -4.80625116 -5.12384955 -5.42200643 -5.69085561 -5.92265826
##  [85] -6.11228048 -6.25705320 -6.35618563 -6.41008742 -6.41995881 -6.38783460
##  [91] -6.31701397 -6.21260203 -6.08182690 -5.93389879 -5.77937815 -5.62920230
##  [97] -5.49359823 -5.38107428 -5.29759214 -5.24593860 -5.22528516 -5.23095198
## [103] -5.25446603 -5.28408786 -5.30601445 -5.30635948 -5.27371015 -5.20164509
## [109] -5.09034566 -4.94663905 -4.78245154 -4.61230501 -4.45072594 -4.31020554
## [115] -4.19993624 -4.12524151 -4.08750408 -4.08443323 -4.11060208 -4.15826320
## [121] -4.21846965 -4.28246730 -4.34319326 -4.39657656 -4.44228856 -4.48370400
## [127] -4.52707679 -4.58017726 -4.65075017 -4.74510704 -4.86703612 -5.01709482
## [133] -5.19229875 -5.38623705 -5.58968171 -5.79175753 -5.98163628 -6.15050243
## [139] -6.29329627 -6.40965218 -6.50365553 -6.58247563 -6.65433540 -6.72642608
## [145] -6.80325690 -6.88570852 -6.97088745 -7.05279092 -7.12372069 -7.17624468
## [151] -7.20528912 -7.20976510 -7.19317221 -7.16294658 -7.12877501 -7.10040356
## [157] -7.08548577 -7.08782924 -7.10620652 -7.13383474 -7.15870249 -7.16501654
## [163] -7.13595174 -7.05743600 -6.92197504 -6.73104449 -6.49496674 -6.23038795
## [169] -5.95657732 -5.69198452 -5.45190479 -5.24736733 -5.08494107 -4.96707879
## [175] -4.89272891 -4.85808304 -4.85742250 -4.88405993 -4.93134567 -4.99364554
## [181] -5.06713262 -5.15021483 -5.24347086 -5.34907802 -5.46983765 -5.60798509
## [187] -5.76399276 -5.93556167 -6.11698853 -6.29911306 -6.47005982 -6.61690650
## [193] -6.72814500 -6.79637557 -6.82032517 -6.80535492 -6.76221653 -6.70457355
## [199] -6.64620064 -6.59863925 -6.56967242 -6.56262530 -6.57635078 -6.60577965
## [205] -6.64298500 -6.67872482 -6.70432931 -6.71361244

plotts.sample.wge(covid$grocery_and_pharmacy_percent_change_from_baseline)

## $autplt
##  [1] 1.0000000 0.5718666 0.4305810 0.3785319 0.3663851 0.3824575 0.4312192
##  [8] 0.5548184 0.4246140 0.3853048 0.3565034 0.3606460 0.4055749 0.4196149
## [15] 0.4525967 0.3931202 0.3714544 0.3381515 0.3342886 0.3607135 0.3832291
## [22] 0.4285594 0.3961949 0.3493541 0.3282081 0.3299540
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  18.773019732  -3.162583574   8.993898242   5.030072262  -0.409756488
##   [6]   2.350008203  -4.305990161   1.842758341  -0.757595242   1.351931965
##  [11]   1.520386459   3.235717694  -2.842935920   0.265444875  -7.916445346
##  [16]   2.019850811   3.007367085  -1.157786686  -3.757999311  -8.838270466
##  [21]  -9.359000699   1.878852393  -3.366243480  -2.280656155  -3.305577002
##  [26]   1.147727986  -5.728775369   0.326235298 -15.974831435  -9.155757653
##  [31]  -8.711484080   2.908127643   3.021403280  -0.207164545  -1.302762649
##  [36]  -8.276039888  -8.184938806  -3.666192053  -6.466930205  -2.216289264
##  [41]   2.735970060   0.071044747  -0.930164633 -13.824831559  -0.887170569
##  [46]  -0.950825351   1.130401949   1.181874908   1.201634899  -6.073732224
##  [51] -15.184566407 -34.183264565 -11.823836487  -2.007452303  -0.009349916
##  [56]   3.995441582   3.202001295   1.115731897   7.175289161   3.067723599
##  [61]   4.486275898   1.259239597   2.089702084  -2.042488864  -1.239393522
##  [66]  -9.239440500  -3.640125269   1.721150915  -7.903932819  -0.920435517
##  [71]  -0.306173787  -0.014994754   0.119778058   1.401319428  -2.348656198
##  [76]  -5.376882645 -30.286077786  -4.914288872  -3.226709501 -12.150223720
##  [81] -12.021709849  -7.167834481  -1.467119727  -0.989459989  -6.098626642
##  [86] -10.843662774  -6.915766477  -3.386845894  -4.327459026 -10.085435505
##  [91]  -6.015232441 -15.247706911  -4.448077073  -1.834738422  -3.268136719
##  [96]  -8.162361319 -10.209504555  -3.491446844  -6.382146318  -3.484469234
## [101]  -1.997805727  -6.891748357  -1.212934332   0.218359859  -1.278307024
## [106]  -1.159807933  -4.909499598  -6.324744163  -8.890319827 -21.965030281
## [111] -10.161023283  -2.429615291   0.717624155   0.936808292  -2.582049102
## [116]  -3.703893255  -4.590650800  -2.336692727   4.559930371  -1.292765344
## [121]  -6.003050336  -0.983250934  -5.302796644 -10.048680883 -10.877659156
## [126]  -6.958936076  -7.886154271  -0.969264605  -0.132859024   1.777886414
## [131]   0.697496399  -5.640497135  -7.718104598 -24.683122902 -26.503391998
## [136] -14.840889512  -8.971879405  -0.177999250  -2.176193382  -8.915555207
## [141]  -4.617606655 -12.470213279  -9.707410219  -6.459800892  -6.093582283
## [146]  -3.418487120  -5.856590155  -9.840778362  -7.350589431 -12.423019028
## [151]  -7.042230462  -9.659772674 -10.068174118  -4.623261152  -4.401595558
## [156] -19.611035861  -9.522602266  -3.741129305  -5.153107967  -8.848913127
## [161]  -2.370487525  -4.338499705  -4.219472546 -10.667172189 -11.647133248
## [166]  -9.577817709  -9.037534263  -9.357544031  -6.343933453  -2.582156018
## [171]  -1.029626126  -2.885439835  -3.459647935   1.001122257  -1.120494045
## [176]  -3.634498144  -0.426626053  -2.366274791  -2.188091234  -5.201642273
## [181] -14.565130067  -5.189152572  -0.877973823  -1.197339269  -1.661047839
## [186]  -1.384901017  -0.792967788  -3.039622266 -13.206280959 -11.522184642
## [191]  -8.080111229 -10.525603897  -9.293773819 -11.580092865  -8.369891339
## [196]  -4.186638135  -5.671966996 -11.328209309  -5.080949562  -2.729439181
## [201]  -3.413405374 -10.386187422  -8.538628979  -4.493992263  -6.158802397
## [206] -10.966064660 -11.874034461 -14.328734005
## 
## $dbz
##   [1] 11.06632233 10.89117632 10.59908748 10.18996064  9.66405160  9.02246472
##   [7]  8.26796764  7.40628112  6.44803341  5.41150485  4.32593951  3.23425506
##  [13]  2.19233241  1.26091909  0.48898519 -0.10406386 -0.53386371 -0.83907289
##  [19] -1.06172751 -1.23293496 -1.36842944 -1.47144180 -1.53885579 -1.56754082
##  [25] -1.55875525 -1.51954947 -1.46138510 -1.39723286 -1.33863105 -1.29366364
##  [31] -1.26612272 -1.25568197 -1.25877226 -1.26986774 -1.28292270 -1.29270102
##  [37] -1.29574143 -1.29075643 -1.27838897 -1.26041202 -1.23858472 -1.21343315
##  [43] -1.18321570 -1.14330642 -1.08621150 -1.00240089 -0.88201229 -0.71720786
##  [49] -0.50459087 -0.24685689  0.04697281  0.36280966  0.68370113  0.99217460
##  [55]  1.27210039  1.50983467  1.69471693  1.81913732  1.87839209  1.87048470
##  [61]  1.79595985  1.65779683  1.46133985  1.21420096  0.92603629  0.60807723
##  [67]  0.27231850 -0.06965030 -0.40802955 -0.73609779 -1.05100109 -1.35373156
##  [73] -1.64824271 -1.93994244 -2.23397313 -2.53367545 -2.83950871 -3.14856990
##  [79] -3.45476997 -3.74966860 -4.02387746 -4.26878307 -4.47815888 -4.64916128
##  [85] -4.78235662 -4.88078158 -4.94841176 -4.98860021 -5.00299138 -4.99120669
##  [91] -4.95135081 -4.88116231 -4.77944876 -4.64734469 -4.48897402 -4.31130673
##  [97] -4.12328868 -3.93454745 -3.75403609 -3.58888883 -3.44361988 -3.31968883
## [103] -3.21541522 -3.12623836 -3.04534541 -2.96468754 -2.87633560 -2.77399508
## [109] -2.65435934 -2.51793169 -2.36906385 -2.21521189 -2.06566358 -1.93010839
## [115] -1.81737034 -1.73447729 -1.68609776 -1.67429456 -1.69852723 -1.75585885
## [121] -1.84135582 -1.94868942 -2.07093550 -2.20151961 -2.33518081 -2.46876437
## [127] -2.60164557 -2.73566112 -2.87455720 -3.02309396 -3.18601677 -3.36709622
## [133] -3.56838142 -3.78974642 -4.02876527 -4.28092922 -4.54019851 -4.79983935
## [139] -5.05342188 -5.29576867 -5.52359595 -5.73563271 -5.93214859 -6.11401427
## [145] -6.28157537 -6.43368551 -6.56721340 -6.67723659 -6.75797107 -6.80426329
## [151] -6.81322796 -6.78546626 -6.72537902 -6.64041326 -6.53948305 -6.43105608
## [157] -6.32139965 -6.21332000 -6.10556195 -5.99294661 -5.86729095 -5.71908520
## [163] -5.53972296 -5.32380658 -5.07085428 -4.78582999 -4.47834553 -4.16090799
## [169] -3.84687164 -3.54868176 -3.27671000 -3.03870042 -2.83968941 -2.68223110
## [175] -2.56679407 -2.49224508 -2.45637279 -2.45642085 -2.48959839 -2.55352453
## [181] -2.64655353 -2.76792653 -2.91771085 -3.09651392 -3.30499041 -3.54318789
## [187] -3.80979765 -4.10139969 -4.41182659 -4.73182769 -5.04927863 -5.35019272
## [193] -5.62065486 -5.84944433 -6.03063278 -6.16516222 -6.26066348 -6.32952360
## [199] -6.38594342 -6.44295638 -6.51009623 -6.59196139 -6.68764623 -6.79096933
## [205] -6.89151450 -6.97654038 -7.03365895 -7.05380883

plotts.sample.wge(covid$parks_percent_change_from_baseline)

## $autplt
##  [1] 1.0000000 0.7440129 0.6495430 0.5132290 0.4732777 0.5043856 0.4955729
##  [8] 0.5909207 0.4750409 0.4689025 0.4107807 0.4139621 0.4814162 0.4599183
## [15] 0.5479859 0.4348813 0.4253223 0.3601215 0.3310964 0.3590276 0.3471454
## [22] 0.4491574 0.3600870 0.3781632 0.3265185 0.3046740
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  18.12171161  14.55252244   1.44610879   8.48672266   7.67812514
##   [6]   5.32610757   0.69341894   0.76387998   2.07369358   5.49054846
##  [11]   4.73787036   3.66478021   0.27713606   0.84219967  -1.19417922
##  [16]  -6.73299185  -6.20106003   1.39538382  -4.55923976   0.39921518
##  [21]  -1.66192022   5.43626047  -2.20172063  -3.16862760  -2.90406608
##  [26]   1.82865885   3.91274183  -7.15606128  -3.63138131  -1.71356719
##  [31]  -7.35719780  -5.90979590  -1.68182559   6.21904714   4.38338758
##  [36]  -3.32559172  -6.29953103   0.56969189  -1.91325996 -12.96920486
##  [41]  -2.59055407  -4.31952598 -10.26416979  -4.51444975  -3.90923373
##  [46]  -4.96140909  -2.55151440 -14.51519226   3.43362914  -6.58984320
##  [51]   1.96577208  -2.96532014  -1.33631164  -1.49530973  -0.23501415
##  [56]  -2.88989747   0.07847912   1.52493266   8.52053903   0.39692148
##  [61]   4.26167550  -7.42658019  -3.76017270  -9.32775166 -15.78231191
##  [66]   1.34864761  -1.83524830 -16.36957208  -3.35476758  -0.18269683
##  [71]  -8.01693216  -4.19733815  -4.87630530 -12.27744380  -7.35908878
##  [76]  -0.58408625 -22.73169092  -5.09740830  -5.32930928 -12.53436384
##  [81]  -3.88366428  -8.50878113  -6.84065761  -6.62417217 -16.77586531
##  [86]  -6.22424534  -8.65880788 -24.49756954 -23.05317994  -6.69957674
##  [91] -10.95525988 -13.70301890  -6.34325843  -0.30807483  -7.08861268
##  [96] -13.96739561  -9.28719355 -11.40868923 -13.52954822 -17.45842472
## [101]  -7.18686964 -11.02750850  -2.75502773  -2.96481474  -6.87243555
## [106]  -8.23729823 -12.64154326  -8.19220636 -19.45310235  -8.88340369
## [111]  -7.80231427 -10.10308458  -8.92519066  -8.41052872 -10.46053792
## [116]  -7.21075546  -2.62344885  -6.11284198   0.01792471  -1.76790371
## [121] -14.58315409  -9.65196168 -18.27066267  -8.68727754  -4.29533682
## [126] -14.06844833 -12.82855841  -8.61831734  -6.16719328 -12.25596580
## [131] -18.25607865  -6.95043201 -14.05490375 -24.44227521 -11.53280041
## [136] -11.93231050 -10.19704446  -3.47711792 -13.55978802  -6.75241241
## [141] -18.37630282  -9.29057579  -6.59537863 -10.33908843 -11.44724467
## [146]  -6.84537381  -6.15044854 -16.93898768 -26.95676352 -20.41191673
## [151]  -7.14586252 -16.89146369 -11.12186630 -14.85651980 -16.80475570
## [156]  -9.79630063 -10.16427254 -10.71073771 -10.72842943 -12.51664456
## [161] -18.66088418 -13.37822885 -11.77612378 -13.68223005  -3.42102719
## [166] -11.20517360 -19.23976665  -9.98681315 -10.71020992 -11.63039934
## [171] -13.41273676 -12.29877934 -10.32322591  -6.56190072  -4.42073130
## [176]  -0.38288564  -5.72482251   7.91583915  -2.28861978  -9.92487674
## [181]  -2.93601986 -12.44277077  -6.11365012 -16.67188194 -13.25625975
## [186] -19.05612764 -13.99618638 -27.50865951 -15.78822387 -30.75454992
## [191]  -5.79678298  -4.95384818 -10.62292835  -7.46069770  -9.39768530
## [196] -23.53152855 -12.10663300  -6.64665350 -16.24747290 -11.19580269
## [201] -17.50631382 -12.46580405  -8.72416839 -14.66298718  -4.92517562
## [206]  -4.85987089 -26.75541638 -18.50828765
## 
## $dbz
##   [1]  11.77581084  11.61943076  11.35912995  10.99556183  10.52997611
##   [6]   9.96461676   9.30332736   8.55243352   7.72196460   6.82721176
##  [11]   5.89042607   4.94205525   4.02032410   3.16759124   2.42274241
##  [16]   1.81161468   1.34043762   0.99666119   0.75651682   0.59426339
##  [21]   0.48847888   0.42408996   0.39135267   0.38360620   0.39515319
##  [26]   0.41992488   0.45102639   0.48092079   0.50190336   0.50658280
##  [31]   0.48822663   0.44095977   0.35988371   0.24120922   0.08248645
##  [36]  -0.11700772  -0.35569173  -0.62891106  -0.92803482  -1.23957825
##  [41]  -1.54469140  -1.81958022  -2.03754406  -2.17300299  -2.20689771
##  [46]  -2.13154293  -1.95259296  -1.68711351  -1.35895302  -0.99375278
##  [51]  -0.61535401  -0.24405797   0.10370322   0.41495388   0.67953026
##  [56]   0.88948032   1.03861126   1.12219798   1.13683188   1.08038509
##  [61]   0.95207289   0.75260457   0.48441628   0.15197257  -0.23789850
##  [66]  -0.67571201  -1.14921106  -1.64363084  -2.14256884  -2.62960060
##  [71]  -3.09051816  -3.51567863  -3.90165958  -4.25151574  -4.57347034
##  [76]  -4.87852338  -5.17778300  -5.48019559  -5.79098667  -6.11081945
##  [81]  -6.43556447  -6.75662120  -7.06183765  -7.33711832  -7.56869519
##  [86]  -7.74573848  -7.86263996  -7.92019530  -7.92524458  -7.88896416
##  [91]  -7.82451557  -7.74484199  -7.66111664  -7.58196953  -7.51336050
##  [96]  -7.45887061  -7.42019258  -7.39764603  -7.39059125  -7.39765793
## [101]  -7.41674950  -7.44483658  -7.47761533  -7.50917409  -7.53187196
## [106]  -7.53665980  -7.51402352  -7.45555615  -7.35587617  -7.21432555
## [111]  -7.03581210  -6.83043781  -6.61205260  -6.39627279  -6.19857905
## [116]  -6.03289616  -5.91076312  -5.84099208  -5.82963374  -5.88007581
## [121]  -5.99314860  -6.16716296  -6.39784994  -6.67821299  -6.99834862
## [126]  -7.34535091  -7.70348380  -8.05485621  -8.38080831  -8.66403538
## [131]  -8.89112246  -9.05478546  -9.15500408  -9.19859192  -9.19741112
## [136]  -9.16595613  -9.11909492  -9.07044808  -9.03150293  -9.01131415
## [141]  -9.01656734  -9.05181145  -9.11972637  -9.22134444  -9.35617745
## [146]  -9.52221942  -9.71581157  -9.93138322 -10.16113277 -10.39479460
## [151] -10.61973668 -10.82169786 -10.98639774 -11.10192758 -11.16128772
## [156] -11.16398089 -11.11564726 -11.02546080 -10.90194320 -10.74840441
## [161] -10.55930636 -10.31885543 -10.00321984  -9.58727016  -9.05459697
## [166]  -8.40633938  -7.66350822  -6.86146691  -6.04055663  -5.23810468
## [171]  -4.48428221  -3.80133609  -3.20465415  -2.70440205  -2.30706521
## [176]  -2.01666054  -1.83559460  -1.76521833  -1.80613476  -1.95829658
## [181]  -2.22090198  -2.59206492  -3.06820203  -3.64304741  -4.30619957
## [186]  -5.04117212  -5.82317354  -6.61742853  -7.37977772  -8.06189177
## [191]  -8.62201573  -9.03763856  -9.31225297  -9.47092040  -9.54787439
## [196]  -9.57430304  -9.57162577  -9.55052990  -9.51360948  -9.45943944
## [201]  -9.38655413  -9.29630989  -9.19407848  -9.08878140  -8.99128911
## [206]  -8.91242448  -8.86117498  -8.84341372

plotts.sample.wge(covid$transit_stations_percent_change_from_baseline)

## $autplt
##  [1] 1.0000000 0.8847764 0.7830763 0.7667176 0.7477690 0.7040921 0.7250004
##  [8] 0.7661085 0.7090003 0.6598821 0.6631634 0.6605950 0.6462659 0.6670185
## [15] 0.7020334 0.6653437 0.6328281 0.6347468 0.6217774 0.6060633 0.6268151
## [22] 0.6583927 0.6187125 0.5822011 0.5805933 0.5694103
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  21.07275612   4.75478331   0.69948673  10.76643105  -8.77438423
##   [6]   8.27918921  -6.81649963   4.16236616   4.63628327  -1.99406315
##  [11]   3.83104458   2.67773075 -12.15663163  -3.10649499  -7.68621103
##  [16]  -0.37674876   3.27068883   0.68352236  -0.66489086   0.70011592
##  [21]  -9.50587172   1.79764887  -4.44529966   0.43839924  -2.86210369
##  [26]   1.50164481  -3.30567221 -15.83676111 -10.62410832  -2.15036161
##  [31]  -2.54317395  -2.20045109  -1.95555585  -4.41671008   0.07189779
##  [36]  -3.77222944 -10.14153542  -6.73614575 -11.00240936  -4.00122162
##  [41]  -5.17833033 -11.22492470 -19.02800005  -6.26616667   0.02541647
##  [46]  -1.01359622  -2.59710849 -14.93327915  -5.70094749  -5.90603877
##  [51]  -8.13865734 -11.68482405 -17.24665002  -3.19838728  -9.74672382
##  [56]   0.15492232   1.37668597  -1.69994630   2.30038521   4.35330987
##  [61]  -9.68102609  -6.59812376  -4.00111848 -15.14199281 -13.37246276
##  [66] -18.33920600  -6.57634259  -9.53387289 -18.82585290  -3.66254227
##  [71]  -5.61399516  -3.81994923  -7.94784825  -4.80764351  -6.45805742
##  [76]  -6.70068904 -12.88710058 -12.54718104 -15.11511024 -14.84342290
##  [81]  -7.77820053 -14.52039255  -7.92401160  -8.97081362  -8.46804901
##  [86]  -7.32797177 -10.79299631 -12.96302443 -12.79786623 -13.54780720
##  [91]  -9.50983355 -25.76307896  -7.77597083  -8.78702877  -7.72426682
##  [96] -14.79486428 -12.29910990  -7.84672680 -15.02082488 -11.04460584
## [101] -10.11320675 -15.48941296  -5.70892096  -5.11161042  -4.26012386
## [106]  -3.27040060 -16.80646694 -12.38053367 -12.18369436 -15.51410832
## [111]  -8.46891666 -16.68240922  -5.66204135  -3.65873533  -7.29537174
## [116] -11.27257385  -8.18932402  -1.47366555   5.52725072 -10.35790857
## [121]  -5.92238127 -10.71007212 -11.15823282 -13.51660957 -23.58209243
## [126] -12.55279278 -12.47065041  -9.18483619  -6.12736486  -6.20483607
## [131]  -6.39978224 -14.47232921 -19.06199539 -19.95286687 -27.31975824
## [136] -27.87631386 -20.20383044 -10.47473030 -13.81714473 -13.87694121
## [141] -11.40509272 -20.89984255 -15.91132250 -10.97558700 -12.63112330
## [146] -18.29494888 -17.00604099 -16.34852101 -17.23522850 -14.58677314
## [151] -19.65576116 -12.73605164 -18.83826880 -17.61742064 -17.48971490
## [156] -16.46170399 -16.80899163 -19.79841371 -31.22428993 -25.86028591
## [161] -11.63774827 -25.18282913 -15.18165066 -20.86161791 -19.82713888
## [166] -14.92140032 -17.66763984 -13.75504202 -25.22397806 -13.60560015
## [171] -18.24273862 -10.17034786 -14.23385039 -11.33125853 -18.03360329
## [176] -15.95470825  -8.98959468  -3.09544060 -17.51031612 -18.54538324
## [181] -22.20343916 -13.40459974 -10.34921986 -13.71477716 -13.26615237
## [186] -12.94928201 -17.13034642 -18.21173232 -21.18039224 -25.60966537
## [191] -26.16205388 -12.85990634 -18.34263356 -15.12028224 -11.51056294
## [196] -14.01949386 -15.34154644 -14.29001531 -14.44464367 -13.26274610
## [201] -14.81972528 -21.31405720 -26.20751706 -18.62356470  -9.66207686
## [206] -16.94348919 -24.70852062 -17.57038658
## 
## $dbz
##   [1]  13.25378361  13.07775368  12.78382951  12.37130807  11.83945405
##   [6]  11.18783212  10.41687649   9.52884606   8.52938909   7.43000635
##  [11]   6.25164763   5.02920101   3.81518777   2.67831472   1.69084986
##  [16]   0.90431446   0.32734549  -0.07479736  -0.35832511  -0.57581088
##  [21]  -0.76294419  -0.93760498  -1.10526293  -1.26574507  -1.41874744
##  [26]  -1.56694846  -1.71655540  -1.87590189  -2.05314891  -2.25407579
##  [31]  -2.48056158  -2.72996770  -2.99541109  -3.26683321  -3.53269937
##  [36]  -3.78202209  -4.00622391  -4.20028639  -4.36280809  -4.49498654
##  [41]  -4.59893342  -4.67591244  -4.72501919  -4.74262671  -4.72273256
##  [46]  -4.65819064  -4.54263724  -4.37269226  -4.14981287  -3.88117912
##  [51]  -3.57930398  -3.26055538  -2.94315240  -2.64525098  -2.38351554
##  [56]  -2.17228162  -2.02320907  -1.94524364  -1.94471035  -2.02540337
##  [61]  -2.18858194  -2.43281932  -2.75368737  -3.14330694  -3.58987267
##  [66]  -4.07738297  -4.58595546  -5.09319265  -5.57690051  -6.01888187
##  [71]  -6.40866740  -6.74554478  -7.03778414  -7.29935501  -7.54559588
##  [76]  -7.78940523  -8.03881684  -8.29606795  -8.55790118  -8.81680537
##  [81]  -9.06294644  -9.28648762  -9.47983489  -9.63921697  -9.76511027
##  [86]  -9.86139330  -9.93357407  -9.98671208 -10.02364798 -10.04396610
##  [91] -10.04390684 -10.01727862  -9.95723921  -9.85856210  -9.71973483
##  [96]  -9.54414784  -9.33989539  -9.11824311  -8.89129533  -8.66954350
## [101]  -8.45980730  -8.26381891  -8.07755712  -7.89146330  -7.69176369
## [106]  -7.46307878  -7.19212342  -6.87162058  -6.50302061  -6.09686143
## [111]  -5.67069442  -5.24564929  -4.84306465  -4.48212212  -4.17868659
## [116]  -3.94507686  -3.79036158  -3.72084840  -3.74055993  -3.85159135
## [121]  -4.05430556  -4.34735252  -4.72751385  -5.18938691  -5.72494781
## [126]  -6.32308293  -6.96926223  -7.64563276  -8.33187940  -9.00711093
## [131]  -9.65265695 -10.25504756 -10.80796951 -11.31217378 -11.77324337
## [136] -12.19819726 -12.59235846 -12.95760475 -13.29244750 -13.59372473
## [141] -13.85917081 -14.08980568 -14.29114270 -14.47273528 -14.64632878
## [146] -14.82339712 -15.01287513 -15.21958894 -15.44354594 -15.68005529
## [151] -15.92059592 -16.15431599 -16.36993805 -16.55765740 -16.71048299
## [156] -16.82454996 -16.89828598 -16.93078013 -16.92003131 -16.86180185
## [161] -16.74960604 -16.57600933 -16.33495792 -16.02439111 -15.64814047
## [166] -15.21634552 -14.74428025 -14.25017481 -13.75289094 -13.27010396
## [171] -12.81723402 -12.40704354 -12.04967859 -11.75293402 -11.52258324
## [176] -11.36267757 -11.27576613 -11.26301290 -11.32419832 -11.45759644
## [181] -11.65971994 -11.92493303 -12.24495489 -12.60832718 -13.00000945
## [186] -13.40139160 -13.79112081 -14.14710188 -14.44967479 -14.68528206
## [191] -14.84928320 -14.94660475 -14.98987536 -14.99593323 -14.98215508
## [196] -14.96369956 -14.95201469 -14.95440749 -14.97428522 -15.01173076
## [201] -15.06420147 -15.12725010 -15.19522947 -15.26196760 -15.32140129
## [206] -15.36814827 -15.39799114 -15.40824571

plotts.sample.wge(covid$workplaces_percent_change_from_baseline)

## $autplt
##  [1]  1.00000000  0.44796635 -0.01288400  0.02633470 -0.03157772 -0.18145143
##  [7]  0.18280104  0.59257819  0.17737026 -0.21615134 -0.12899263 -0.13549646
## [13] -0.24339479  0.11873042  0.51357580  0.12541975 -0.22990665 -0.12521062
## [19] -0.13258143 -0.23271999  0.12620792  0.51218310  0.12714698 -0.22630753
## [25] -0.11306640 -0.10286350
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]   7.06242102   8.65869199   1.79225738 -16.32912737   0.50166223
##   [6]   1.89915277  -4.35989604   3.65331325   6.24581602   4.19342188
##  [11]   3.18780981   1.22252444   1.73312254   1.53654600   5.12252156
##  [16]   7.50974273   4.06825924  -2.22329651   0.03655859  -1.07893693
##  [21]  -0.49806934 -25.15427724 -11.99945484   1.54112504   4.37053882
##  [26]   1.91026186   2.93510327  -9.36837172   0.46337190   2.00279620
##  [31]   0.58880390  -4.36022558  -4.26194105  -3.87495061   0.85091904
##  [36]   0.30308088  -0.79560396 -21.42788568  -3.23037815  -1.55929723
##  [41]  -2.32259361 -21.62982080 -10.95732727  -1.77756879   4.09792471
##  [46]   1.55696320   1.74442993  -8.26883352  -8.02735157  -1.28587736
##  [51]  -3.99048721  -7.76905919  -6.69872645   0.80790046  -6.01206349
##  [56]   3.66206743   0.27096449   6.53805667  14.52646677  14.21916351
##  [61]   3.85306894  -3.30049155  -3.47608764 -13.69816723  -5.40751094
##  [66]  -7.06113162  -3.72837620  -7.76801007  -7.80593942  -3.96346089
##  [71]  -3.75811091   0.01849825 -10.86957801 -10.03974614  -9.24331540
##  [76]  -5.56243484 -19.23671114 -23.15200947 -19.29555243  -8.32132803
##  [81]  -7.51645676 -12.14204202  -7.67743186 -31.74178913  -3.53505619
##  [86] -17.28175444  -9.96200797 -10.47708442 -14.10155331 -15.15491855
##  [91] -14.34470430 -11.20240379  -8.73067731  -3.55246964 -16.11761276
##  [96] -16.74895173  -9.60191867  -7.33633192 -14.27249013 -15.18147983
## [101]  -6.05335186  -9.34182299  -3.48813226  -3.59544092 -10.99215114
## [106]  -1.66679361  -9.58798576 -14.39727423 -11.74675201  -7.26946671
## [111]  -8.88029325 -10.86419471  -5.52268328  -2.86292467  -9.95572141
## [116] -21.38234053   1.58352700   3.71457029  16.06320393  -2.57944621
## [121]  -5.43136617  -9.66264670 -16.23262677  -6.86856777 -33.63813770
## [126] -10.71162684  -5.99934344  -4.97012645  -6.97226796  -5.72884143
## [131]  -9.39291191  -3.67014917 -26.13502818 -13.57241430  -7.75911382
## [136] -29.99017213 -21.68504047 -15.11235698  -7.69164048 -13.51013056
## [141]  -4.47086703 -21.04059046 -11.37569671  -8.24128417  -6.81955519
## [146] -17.96743839 -13.58556875  -7.17484674 -16.04817852 -12.58331929
## [151]  -9.28604189 -21.17971790  -4.37152576  -9.50890876 -22.86847327
## [156]  -9.77374669  -7.95140248  -8.42472305 -24.33389517 -17.31506638
## [161]  -8.16914668 -14.54536059 -20.44657872  -8.01566226 -11.74488869
## [166]  -6.39206913 -12.80723926 -18.96329573  -6.58404635  -8.20378816
## [171]  -8.60517404 -27.14068363  -9.58619266 -10.78669041 -10.63747422
## [176] -14.25244443  -9.50593306   5.32762500  -7.73287327  -6.66083014
## [181] -16.03894334 -10.96361976  -5.37487805 -12.18665205 -24.28596367
## [186]  -6.80205101 -17.03315716  -7.99172674 -21.58658802 -10.35494516
## [191]  -4.68243590 -15.43522906 -10.64829086 -12.05361379 -13.17044965
## [196]  -6.78836134 -13.24202446 -10.94283319  -7.25685411 -11.77930691
## [201] -13.95856522 -20.75620249  -9.07400913  -6.21881257  -8.23412856
## [206] -22.68694272  -9.85314923 -22.79718969
## 
## $dbz
##   [1]   4.27575543   4.23001059   4.15783386   4.06487447   3.95812315
##   [6]   3.84498555   3.73217575   3.62461069   3.52455559   3.43125465
##  [11]   3.34116051   3.24869867   3.14735819   3.03085242   2.89414181
##  [16]   2.73420175   2.55049555   2.34514708   2.12280317   1.89015823
##  [21]   1.65511665   1.42562311   1.20830433   1.00719924   0.82292672
##  [26]   0.65257277   0.49037431   0.32903349   0.16134392  -0.01820069
##  [31]  -0.21206335  -0.41875560  -0.63251836  -0.84377805  -1.04054717
##  [36]  -1.21073583  -1.34489159  -1.43836740  -1.49175232  -1.50890019
##  [41]  -1.49285753  -1.44087538  -1.34023610  -1.16704242  -0.89027975
##  [46]  -0.48207023   0.06916503   0.75030103   1.52583806   2.34886665
##  [51]   3.17300690   3.95973848   4.68052984   5.31581698   5.85286998
##  [56]   6.28368353   6.60329913   6.80860058   6.89749689   6.86838958
##  [61]   6.71984160   6.45039355   6.05850097   5.54259325   4.90128598
##  [66]   4.13381923   3.24085266   2.22582927   1.09720886  -0.12810869
##  [71]  -1.42015204  -2.73119642  -3.99481393  -5.13526439  -6.09081956
##  [76]  -6.84021861  -7.40954547  -7.85157643  -8.21595350  -8.53061773
##  [81]  -8.79909971  -9.00873678  -9.14395318  -9.19887165  -9.18363361
##  [86]  -9.12196141  -9.04277338  -8.97117560  -8.92236153  -8.89902852
##  [91]  -8.89160881  -8.88088919  -8.84311920  -8.75727887  -8.61253906
##  [96]  -8.41247942  -8.17345105  -7.91754426  -7.66307869  -7.41540511
## [101]  -7.15951567  -6.85620794  -6.44616640  -5.86764892  -5.08548285
## [106]  -4.11288179  -3.00667249  -1.84133684  -0.68438366   0.41456229
## [111]   1.42365895   2.32442713   3.10711017   3.76716540   4.30294311
## [116]   4.71424822   5.00147951   5.16512562   5.20547698   5.12247000
## [121]   4.91561848   4.58401408   4.12640025   3.54134822   2.82759752
## [126]   1.98467558   1.01399441  -0.07925659  -1.28296690  -2.57325415
## [131]  -3.90806609  -5.22165122  -6.42685808  -7.43497718  -8.19179295
## [136]  -8.70375306  -9.02712298  -9.23128291  -9.36905827  -9.46800440
## [141]  -9.53612617  -9.57234490  -9.57578556  -9.55106827  -9.50899569
## [146]  -9.46389955  -9.42984078  -9.41748584  -9.43245449  -9.47510060
## [151]  -9.54134626  -9.62416541  -9.71535806  -9.80725450  -9.89397193
## [156]  -9.97190529 -10.03931612 -10.09513597 -10.13731297 -10.16113696
## [161] -10.15800887 -10.11514006 -10.01665983  -9.84640602  -9.59206551
## [166]  -9.24941322  -8.82483427  -8.33487618  -7.80310828  -7.25585714
## [171]  -6.71849334  -6.21313123  -5.75772855  -5.36613572  -5.04861047
## [176]  -4.81245541  -4.66259003  -4.60197297  -4.63184509  -4.75178454
## [181]  -4.95956855  -5.25083657  -5.61855765  -6.05233871  -6.53769013
## [186]  -7.05551045  -7.58224783  -8.09133308  -8.55631022  -8.95536277
## [191]  -9.27580431  -9.51645001  -9.68655519  -9.80187967  -9.87984824
## [196]  -9.93570047  -9.98046246 -10.02058753 -10.05868309 -10.09474030
## [201] -10.12743577 -10.15522902 -10.17710103 -10.19288332 -10.20321814
## [206] -10.20925892 -10.21225190 -10.21313424

plotts.sample.wge(covid$residential_percent_change_from_baseline)

## $autplt
##  [1] 1.00000000 0.60506428 0.28381540 0.25769045 0.22694571 0.18127506
##  [7] 0.42684145 0.67222082 0.39051067 0.11514642 0.10670713 0.09032471
## [13] 0.08306564 0.32639794 0.57256582 0.32697503 0.08650950 0.09635481
## [19] 0.08226207 0.06967052 0.30673273 0.55017876 0.31470706 0.08028669
## [25] 0.08853732 0.08644141
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  16.3778740  10.9114585   2.7520869   3.6174364  -1.2386453   5.1380969
##   [7]  -9.1017222   5.9408238   6.1204484   1.0549557   4.5470144   4.9184079
##  [13]  -1.6533875   2.2080740   1.7378020   4.3228212   4.4224081   0.6997466
##  [19]   0.5580162   1.4369829  -5.1120485  -2.2641882  -5.0648638   1.0139991
##  [25]  -0.6195190   2.0462611   1.1982441 -10.1621006  -6.9748443  -0.5685575
##  [31]  -5.4293556  -3.2073763  -2.8654950 -13.7572844   0.9901236  -4.0432531
##  [37]  -5.1929505  -7.2912122 -15.2805598  -3.2783757 -10.5139938 -11.5872588
##  [43] -17.5029264  -4.3306813   1.1862602  -1.4042093  -4.3414281 -11.5891389
##  [49]  -1.0541733   1.0458701  -5.8859789  -8.4272169  -4.7342544  -4.3788435
##  [55]  -8.1701348   4.3722944   2.1278009   5.8201526  12.5911126  13.5517056
##  [61]  -5.7413541  -4.8721425  -3.4123985  -5.1076896  -5.6089282 -16.5854105
##  [67]  -1.8497855 -12.9367079 -17.6421634  -0.4400242  -3.6544555  -2.2819690
##  [73]  -8.7718581  -9.3217243  -5.4993003  -3.9773070 -12.2054656 -22.8764215
##  [79] -25.2263992  -8.4898883 -10.8483000  -7.4206548  -4.2264391 -12.0749431
##  [85]  -5.2657286 -11.3971318 -19.0104246  -6.3797482 -13.9634774 -17.4438232
##  [91] -17.9195119 -13.2238189  -5.7336983  -1.7181897 -10.3557433 -12.0249564
##  [97] -11.6531224  -6.3397268 -15.5340535 -16.1878553  -7.2515603  -7.5227429
## [103]  -5.6058040  -6.0904369  -8.1970915  -1.2992570 -11.8688344 -19.8196235
## [109] -10.6809122  -6.3615510  -7.0387904 -10.5656818  -5.6230125  -3.9999735
## [115]  -8.6133229 -18.4337345  -5.0844725   2.4772154  13.5562443  -9.3245116
## [121]  -7.4471893  -9.1463631 -12.0187035 -10.8315324 -11.7589324 -20.7429618
## [127]  -5.4283603  -5.4998712  -3.4902268  -5.9958660  -7.5182334  -3.9498768
## [133] -17.1337027 -12.2974911  -7.0680983 -12.4511535 -18.5338382 -12.8824046
## [139]  -7.9118653 -13.7645725  -4.3720303 -20.1070723  -8.9322585  -6.6319805
## [145]  -8.2957586 -22.4030101 -13.2268873 -10.7439029 -25.2027162 -13.6701807
## [151]  -6.7300977 -16.1129704  -6.5715726 -10.0792304 -20.6910906 -10.1744365
## [157] -11.4714190  -9.6689978 -28.5094447 -13.8455730 -11.3834431 -12.7874390
## [163] -12.8262003 -10.3250335 -11.0013693  -5.0932254 -18.0258942 -19.7562009
## [169] -11.6006735  -7.8957558  -9.0694014 -13.3980379  -7.1301438  -5.5984021
## [175] -12.6131839 -20.0336593 -13.7160746   4.6367653  -9.0887906 -12.0726144
## [181] -31.9855610 -10.6290041  -6.3649174  -8.8331869 -13.0521184  -6.4397074
## [187] -20.7310298  -9.2845866 -18.2558912 -12.5308938  -7.8352234 -14.2379073
## [193]  -9.1011572 -12.8870084 -11.8181276  -7.6285363 -13.9201634  -9.7454996
## [199]  -6.1827376 -10.4026103 -10.1117223 -17.7831768  -7.8354297  -9.1222443
## [205]  -5.7641523 -18.1011122 -11.8702262 -20.7516956
## 
## $dbz
##   [1]   9.66730178   9.52174976   9.28103068   8.94823581   8.52828275
##   [6]   8.02851337   7.45942734   6.83542791   6.17530635   5.50199848
##  [11]   4.84103116   4.21729167   3.65052793   3.15109965   2.71803528
##  [16]   2.34054854   2.00229322   1.68634980   1.37911301   1.07228902
##  [21]   0.76310767   0.45322727   0.14684370  -0.15150840  -0.43895700
##  [26]  -0.71560536  -0.98482395  -1.25249400  -1.52548673  -1.80982113
##  [31]  -2.10891362  -2.42221122  -2.74441394  -3.06549086  -3.37170953
##  [36]  -3.64776161  -3.87962553  -4.05714254  -4.17486457  -4.23013340
##  [41]  -4.21862753  -4.12916839  -3.94077513  -3.62529472  -3.15723643
##  [46]  -2.52752869  -1.75267059  -0.87234275   0.06239380   1.00184938
##  [51]   1.90532047   2.74307148   3.49502132   4.14835202   4.69522557
##  [56]   5.13100531   5.45299966   5.65962233   5.74985355   5.72291151
##  [61]   5.57807512   5.31462677   4.93190961   4.42951944   3.80768224
##  [66]   3.06790769   2.21405879   1.25402394   0.20216950  -0.91745418
##  [71]  -2.06786728  -3.19804272  -4.24778232  -5.16165706  -5.90821271
##  [76]  -6.49159804  -6.94512556  -7.31168389  -7.62522422  -7.90189768
##  [81]  -8.14064932  -8.32980486  -8.45626702  -8.51395364  -8.50821645
##  [86]  -8.45475062  -8.37445216  -8.28737467  -8.20828531  -8.14463084
##  [91]  -8.09657123  -8.05846596  -8.02133117  -7.97583986  -7.91525756
##  [96]  -7.83746757  -7.74526882  -7.64457444  -7.54076831  -7.43392363
## [101]  -7.31381729  -7.15613190  -6.92234062  -6.56673673  -6.05195684
## [106]  -5.36699244  -4.53530461  -3.60644400  -2.63848194  -1.68339095
## [111]  -0.78063214   0.04291218   0.77027611   1.39138155   1.90057506
## [116]   2.29488434   2.57287125   2.73391343   2.77777826   2.70439801
## [121]   2.51379478   2.20613613   1.78193215   1.24241399   0.59016907
## [126]  -0.16985455  -1.02883434  -1.97194067  -2.97567880  -4.00537848
## [131]  -5.01461281  -5.94948481  -6.75995632  -7.41538391  -7.91487255
## [136]  -8.28411689  -8.56112748  -8.78118097  -8.96847224  -9.13506056
## [141]  -9.28421510  -9.41521925  -9.52762953  -9.62383166  -9.70952356
## [146]  -9.79251186  -9.88068656  -9.98005827 -10.09342864 -10.21989611
## [151] -10.35515239 -10.49240738 -10.62371319 -10.74138868 -10.83919086
## [156] -10.91290363 -10.96016361 -10.97958145 -10.96944801 -10.92645050
## [161] -10.84484972 -10.71651298 -10.53205287 -10.28303153  -9.96473817
## [166]  -9.57861109  -9.13331430  -8.64400035  -8.13012070  -7.61270487
## [171]  -7.11200214  -6.64595101  -6.22949387  -5.87450770  -5.59007518
## [176]  -5.38287873  -5.25757962  -5.21710628  -5.26281295  -5.39448537
## [181]  -5.61017345  -5.90582989  -6.27473942  -6.70675076  -7.18739927
## [186]  -7.69716090  -8.21131529  -8.70112740  -9.13701043  -9.49362239
## [191]  -9.75546154  -9.92041486  -9.99928608 -10.01159043  -9.97990453
## [196]  -9.92517231  -9.86406178  -9.80818768  -9.76448081  -9.73603985
## [201]  -9.72305905  -9.72365628  -9.73456836  -9.75174519  -9.77088777
## [206]  -9.78795734  -9.79965001  -9.80379918

plotts.sample.wge(covid$mobility_mean)

## $autplt
##  [1] 1.0000000 0.7746703 0.6656403 0.6427164 0.6028464 0.5313645 0.5459950
##  [8] 0.6161376 0.5065324 0.4744108 0.5103607 0.5114472 0.4819182 0.4871361
## [15] 0.5540000 0.4659353 0.4394488 0.4706877 0.4558524 0.4091453 0.4159285
## [22] 0.4987903 0.4361481 0.4104534 0.4373936 0.4390635
## 
## $freq
##   [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
##   [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
##  [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
##  [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
##  [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
##  [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
##  [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
##  [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
##  [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
##  [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
##  [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
##  [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
##  [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
##  [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
##  [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
##  [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
##  [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
## 
## $db
##   [1]  19.4590744  11.5047220   4.2706220   8.8818733   1.7815863   7.3556251
##   [7]  -5.6380415   3.3417920   5.5912176   2.9010450   4.9431953   4.2820147
##  [13]  -5.2351493   2.1008489  -0.1280291   0.5485545   3.2448561   2.3475387
##  [19]   0.3210218   1.3707009  -4.2386145   3.4512580  -2.0845859  -2.1833902
##  [25]  -3.5484753   3.9277790   1.5400911  -7.1316995 -15.1506191  -1.1619671
##  [31]  -1.6477689  -0.7976408   1.3750036   1.7423299   3.8633798  -2.8165309
##  [37]  -2.8775211  -3.1470770  -9.3394435  -2.4537467  -5.8429269 -15.7256625
##  [43] -11.6043949  -4.3820916   1.3124995  -0.2811343  -3.6999323  -5.6146837
##  [49]   0.4121339 -14.6007161  -2.6936006  -8.2923814  -4.8307606 -11.4485852
##  [55] -19.5244255   2.8352715   1.1513844  -2.1435576   0.6485969  -0.3094943
##  [61]  -1.6522891  -2.1939743   0.1580610  -7.3553929 -14.4289766  -9.4970576
##  [67]  -2.8398500  -7.8338258 -17.9897088   0.4064696  -2.6452502  -5.2538989
##  [73]  -4.2466983  -3.9317018  -4.7214779  -2.5964379 -19.7222448  -5.6882367
##  [79]  -6.1676781 -11.3026911 -17.8766979  -9.6370210  -4.5489082  -7.1841838
##  [85]  -9.3834122  -8.6942216 -12.2237174  -9.6314332 -13.7216924 -19.8712442
##  [91] -16.3897091 -29.8342367  -4.7110309  -2.2737520  -5.9998915 -15.6689463
##  [97] -11.5278146 -10.7363636 -12.0739523  -7.5648109  -4.5359461 -15.2843799
## [103] -10.8003367 -10.7489697  -4.8532980  -3.7665504 -23.2465290  -9.2900140
## [109] -17.1314533 -11.6684705 -10.2739876  -6.9373562  -3.6740623  -4.4646553
## [115]  -7.8954159  -7.8070138 -10.2464384   0.4696415   8.6047512  -4.0616987
## [121] -10.0747589  -6.9161238 -15.0677557 -22.1798995 -13.1923826 -11.5426030
## [127]  -7.5308397  -9.0004327  -3.2656152  -2.5428778  -7.2814615  -6.8377400
## [133] -19.1161403 -20.9429643 -19.1415751 -17.9736993 -12.0761565  -4.9020897
## [139]  -6.4807408  -9.8277847  -7.7797817 -26.8790598  -7.5430078 -13.0478550
## [145] -11.6595160  -9.4393028  -7.8707698 -11.2727939 -15.1146464 -13.5303325
## [151]  -8.7025348 -15.5089793 -10.1745681  -8.8933312 -11.7768012 -20.3364041
## [157] -12.3464690  -8.1116934 -19.5344533 -17.9910712  -8.4011083 -16.5135652
## [163] -11.3471906 -22.8338096  -9.7092358 -11.1331026 -15.3607456 -12.7286150
## [169] -15.7020537  -6.5840216  -9.5009671 -10.9288616  -7.2220952  -3.1103121
## [175]  -7.2218142 -17.4022277 -10.5007304   3.8823798 -11.9739824  -9.8879132
## [181] -13.3747191 -10.9961676  -4.1539554  -7.1430599 -10.1004782  -7.9261476
## [187] -10.1852357  -9.3158117 -21.7651756 -16.3998358 -21.8851154 -10.6370617
## [193] -11.9399962 -10.2253670 -13.4935072  -8.1324885  -8.5264885  -8.9493962
## [199]  -9.4249928  -7.4101842  -9.8504002 -12.2516917 -12.9930213 -11.6305059
## [205]  -5.6913251  -9.6971565 -15.9003756 -29.1984333
## 
## $dbz
##   [1]  12.20459483  12.04081039  11.76820076  11.38751432  10.90023881
##   [6]  10.30912945   9.61901638   8.83797766   7.97893025   7.06154375
##  [11]   6.11400895   5.17352664   4.28368460   3.48717780   2.81494234
##  [16]   2.27692656   1.86079657   1.53971708   1.28384444   1.06917418
##  [21]   0.88114693   0.71389343   0.56712183   0.44239161   0.34000042
##  [26]   0.25721642   0.18804704   0.12420486   0.05662173  -0.02311305
##  [31]  -0.12175933  -0.24395743  -0.39217422  -0.56688504  -0.76682570
##  [36]  -0.98920084  -1.22979794  -1.48301920  -1.74189754  -1.99820004
##  [41]  -2.24272849  -2.46588753  -2.65850365  -2.81276259  -2.92304478
##  [46]  -2.98643941  -3.00283118  -2.97462374  -2.90628992  -2.80394662
##  [51]  -2.67505390  -2.52821050  -2.37294218  -2.21938576  -2.07783563
##  [56]  -1.95819020  -1.86937375  -1.81880586  -1.81196157  -1.85203487
##  [61]  -1.93970202  -2.07298740  -2.24725865  -2.45541266  -2.68834092
##  [66]  -2.93575647  -3.18739694  -3.43448006  -3.67112048  -3.89531665
##  [71]  -4.10918224  -4.31833327  -4.53062751  -4.75462530  -4.99812779
##  [76]  -5.26700539  -5.56436632  -5.89001226  -6.24010798  -6.60704082
##  [81]  -6.97953678  -7.34319825  -7.68167467  -7.97858934  -8.22005949
##  [86]  -8.39723098  -8.50796943  -8.55701586  -8.55454232  -8.51372919
##  [91]  -8.44826924  -8.37049273  -8.29037182  -8.21529698  -8.15033559
##  [96]  -8.09864443  -8.06174043  -8.03939611  -8.02901144  -8.02444203
## [101]  -8.01447469  -7.98148920  -7.90132530  -7.74573089  -7.48830519
## [106]  -7.11286961  -6.62049106  -6.03084667  -5.37699187  -4.69691017
## [111]  -4.02623533  -3.39429366  -2.82315344  -2.32839586  -1.92049122
## [116]  -1.60615279  -1.38942095  -1.27242980  -1.25588592  -1.33930269
## [121]  -1.52102324  -1.79804851  -2.16567368  -2.61693550  -3.14189583
## [126]  -3.72685298  -4.35370087  -4.99984371  -5.63923846  -6.24506245
## [131]  -6.79391444  -7.27037906  -7.66993970  -7.99864730  -8.26968286
## [136]  -8.49859911  -8.69929317  -8.88182787  -9.05212175  -9.21291622
## [141]  -9.36529098  -9.51010510  -9.64894106  -9.78437162  -9.91961105
## [146] -10.05778886 -10.20114918 -10.35043816 -10.50464186 -10.66112498
## [151] -10.81611981 -10.96542742 -11.10512593 -11.23205185 -11.34385555
## [156] -11.43853542 -11.51350366 -11.56438925 -11.58391798 -11.56131986
## [161] -11.48277506 -11.33330875 -11.10011183 -10.77647906 -10.36484005
## [166]  -9.87743809  -9.33432430  -8.75969516  -8.17815430  -7.61202184
## [171]  -7.07998817  -6.59683573  -6.17378222  -5.81907397  -5.53860114
## [176]  -5.33642336  -5.21516578  -5.17627843  -5.22016215  -5.34616195
## [181]  -5.55242060  -5.83557642  -6.19028374  -6.60854295  -7.07886488
## [186]  -7.58538850  -8.10724981  -8.61874930  -9.09105351  -9.49596561
## [191]  -9.81136562 -10.02647597 -10.14435985 -10.18021013 -10.15640631
## [196] -10.09686020 -10.02275725  -9.95037700  -9.89059184  -9.84931902
## [201]  -9.82835067  -9.82625089  -9.83921381  -9.86188593  -9.88818961
## [206]  -9.91216447  -9.92879391  -9.93472930

Look at cross correlation of each variable

par(mfrow=c(1,1))
covid_d1=artrans.wge(covid$case_count,1)

covid_d1s7=artrans.wge(covid_d1,c(rep(0,6),1))

Ccf(covid_d1,artrans.wge(covid$tests_taken,c(1)),lag.max = 40) #Differenced Lag 4

Ccf(covid_d1,artrans.wge(covid$vaccine_doses_administered,c(1)),lag.max = 40) #Seasonal trend remaining

Ccf(covid_d1,artrans.wge(artrans.wge(covid$vaccine_doses_administered,c(1)),c(rep(0,6),1)),lag.max = 40) #Diff and Seas Lag 19

Ccf(covid_d1,artrans.wge(covid$retail_and_recreation_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1

Ccf(covid_d1,artrans.wge(covid$grocery_and_pharmacy_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1

Ccf(covid_d1,artrans.wge(covid$parks_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Insignificant

Ccf(covid_d1,artrans.wge(covid$transit_stations_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1

Ccf(covid_d1,artrans.wge(covid$workplaces_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 0/ Lag 1

Ccf(covid_d1,artrans.wge(covid$residential_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag -1,0,1

Ccf(covid_d1,artrans.wge(covid$mobility_mean,c(rep(0,6),1)),lag.max = 40) #Lag -1

Create VAR Model

#Create first differenced data set and reduce attributes
covid_d1=covid[,2:dim(covid)[2]]
for (i in c(1:(dim(covid)[2]-1))){
  covid_d1[,i]=c(NA,artrans.wge(x = covid_d1[,i],1))
}

names(covid_d1)

##  [1] "tests_taken"                                       
##  [2] "case_count"                                        
##  [3] "retail_and_recreation_percent_change_from_baseline"
##  [4] "grocery_and_pharmacy_percent_change_from_baseline" 
##  [5] "parks_percent_change_from_baseline"                
##  [6] "transit_stations_percent_change_from_baseline"     
##  [7] "workplaces_percent_change_from_baseline"           
##  [8] "residential_percent_change_from_baseline"          
##  [9] "vaccine_doses_administered"                        
## [10] "mobility_mean"

str(covid)

## 'data.frame':    416 obs. of  11 variables:
##  $ Date                                              : Date, format: "2020-09-14" "2020-09-15" ...
##  $ tests_taken                                       : int  34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
##  $ case_count                                        : int  3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
##  $ retail_and_recreation_percent_change_from_baseline: int  -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
##  $ grocery_and_pharmacy_percent_change_from_baseline : int  -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
##  $ parks_percent_change_from_baseline                : int  1 7 7 16 6 21 -6 -29 -28 -9 ...
##  $ transit_stations_percent_change_from_baseline     : int  -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
##  $ workplaces_percent_change_from_baseline           : int  -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
##  $ residential_percent_change_from_baseline          : int  9 10 10 10 9 3 4 12 15 12 ...
##  $ vaccine_doses_administered                        : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ mobility_mean                                     : num  -13.2 -11.3 -11 -10.2 -11 ...

str(covid_d1)

## 'data.frame':    416 obs. of  10 variables:
##  $ tests_taken                                       : num  NA 22426 -6246 53752 19203 ...
##  $ case_count                                        : num  NA 1372 684 -1979 -625 ...
##  $ retail_and_recreation_percent_change_from_baseline: num  NA 2 0 -1 0 0 -1 -4 -1 5 ...
##  $ grocery_and_pharmacy_percent_change_from_baseline : num  NA 3 0 -2 2 3 -4 -5 0 5 ...
##  $ parks_percent_change_from_baseline                : num  NA 6 0 9 -10 15 -27 -23 1 19 ...
##  $ transit_stations_percent_change_from_baseline     : num  NA 0 1 0 2 5 -6 -6 -3 5 ...
##  $ workplaces_percent_change_from_baseline           : num  NA -1 1 -1 2 18 -2 -20 -3 6 ...
##  $ residential_percent_change_from_baseline          : num  NA 1 0 0 -1 -6 1 8 3 -3 ...
##  $ vaccine_doses_administered                        : num  NA 0 0 0 0 0 0 0 0 0 ...
##  $ mobility_mean                                     : num  NA 1.833 0.333 0.833 -0.833 ...

covid_d1=covid_d1[2:dim(covid_d1)[1],c(1,2,9,10)]

#Create reduced variable covid data set to mob mean, vax, test count, and case count
names(covid)

##  [1] "Date"                                              
##  [2] "tests_taken"                                       
##  [3] "case_count"                                        
##  [4] "retail_and_recreation_percent_change_from_baseline"
##  [5] "grocery_and_pharmacy_percent_change_from_baseline" 
##  [6] "parks_percent_change_from_baseline"                
##  [7] "transit_stations_percent_change_from_baseline"     
##  [8] "workplaces_percent_change_from_baseline"           
##  [9] "residential_percent_change_from_baseline"          
## [10] "vaccine_doses_administered"                        
## [11] "mobility_mean"

covid_reduced=covid[,c(2,3,10,11)]

#Test original data set
VARselect(covid_reduced,lag.max = 45,type = 'const')

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      8      8      8      8 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.191644e+01 6.156413e+01 6.138383e+01 6.126674e+01 6.118286e+01
## HQ(n)  6.200029e+01 6.171506e+01 6.160184e+01 6.155182e+01 6.153502e+01
## SC(n)  6.212756e+01 6.194414e+01 6.193274e+01 6.198453e+01 6.206954e+01
## FPE(n) 7.761992e+26 5.457307e+26 4.557331e+26 4.054321e+26 3.728956e+26
##                   6            7            8            9           10
## AIC(n) 6.053240e+01 6.022312e+01 5.984215e+01 5.986445e+01 5.986167e+01
## HQ(n)  6.095164e+01 6.070944e+01 6.039555e+01 6.048493e+01 6.054922e+01
## SC(n)  6.158798e+01 6.144759e+01 6.123552e+01 6.142671e+01 6.159282e+01
## FPE(n) 1.946438e+26 1.429295e+26 9.770909e+25 9.999000e+25 9.980802e+25
##                  11           12           13           14           15
## AIC(n) 5.988675e+01 5.990158e+01 5.992411e+01 5.992668e+01 5.991314e+01
## HQ(n)  6.064139e+01 6.072330e+01 6.081291e+01 6.088255e+01 6.093609e+01
## SC(n)  6.178679e+01 6.197052e+01 6.216194e+01 6.233340e+01 6.248875e+01
## FPE(n) 1.024636e+26 1.041414e+26 1.066917e+26 1.071729e+26 1.059687e+26
##                  16           17           18           19           20
## AIC(n) 5.995070e+01 5.995843e+01 5.998118e+01 6.003426e+01 6.002764e+01
## HQ(n)  6.104073e+01 6.111554e+01 6.120537e+01 6.132552e+01 6.138599e+01
## SC(n)  6.269521e+01 6.287183e+01 6.306348e+01 6.328544e+01 6.344772e+01
## FPE(n) 1.103074e+26 1.114871e+26 1.144276e+26 1.211089e+26 1.208049e+26
##                  21           22           23           24           25
## AIC(n) 6.006241e+01 6.001113e+01 6.001879e+01 6.005369e+01 6.010913e+01
## HQ(n)  6.148783e+01 6.150363e+01 6.157837e+01 6.168035e+01 6.180287e+01
## SC(n)  6.365138e+01 6.376900e+01 6.394554e+01 6.414934e+01 6.437367e+01
## FPE(n) 1.256483e+26 1.199686e+26 1.215597e+26 1.266425e+26 1.347491e+26
##                  26           27           28           29           30
## AIC(n) 6.013599e+01 6.017135e+01 6.021626e+01 6.025958e+01 6.027745e+01
## HQ(n)  6.189681e+01 6.199925e+01 6.211123e+01 6.222163e+01 6.230659e+01
## SC(n)  6.456943e+01 6.477368e+01 6.498748e+01 6.519969e+01 6.538646e+01
## FPE(n) 1.394189e+26 1.455725e+26 1.535552e+26 1.618304e+26 1.663875e+26
##                  31           32           33           34           35
## AIC(n) 6.032199e+01 6.032185e+01 6.034780e+01 6.031458e+01 6.030017e+01
## HQ(n)  6.241820e+01 6.248514e+01 6.257817e+01 6.261203e+01 6.266470e+01
## SC(n)  6.559989e+01 6.576865e+01 6.596348e+01 6.609916e+01 6.625364e+01
## FPE(n) 1.758284e+26 1.778287e+26 1.847592e+26 1.810911e+26 1.810328e+26
##                  36           37           38           39           40
## AIC(n) 6.033013e+01 6.035409e+01 6.033039e+01 6.025304e+01 6.024133e+01
## HQ(n)  6.276174e+01 6.285278e+01 6.289615e+01 6.288588e+01 6.294125e+01
## SC(n)  6.645250e+01 6.664535e+01 6.679054e+01 6.688208e+01 6.703927e+01
## FPE(n) 1.893685e+26 1.971016e+26 1.958096e+26 1.845708e+26 1.859980e+26
##                  41           42           43           44           45
## AIC(n) 6.021520e+01 6.017131e+01 6.020696e+01 6.018890e+01 6.015658e+01
## HQ(n)  6.298220e+01 6.300539e+01 6.310812e+01 6.315714e+01 6.319189e+01
## SC(n)  6.718203e+01 6.730704e+01 6.751158e+01 6.766241e+01 6.779898e+01
## FPE(n) 1.849788e+26 1.809595e+26 1.919418e+26 1.932174e+26 1.920325e+26

  #AIC 8, BIC 8

#Fit based on AIC
fit1a=VAR(covid_reduced,p=8,type="const")
summary(fit1a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean 
## Deterministic variables: const 
## Sample size: 408 
## Log Likelihood: -14342.058 
## Roots of the characteristic polynomial:
## 0.9897 0.9897 0.9873 0.9873 0.9839 0.9839 0.9477 0.9477 0.9271 0.9271 0.9175 0.907 0.907 0.838 0.8085 0.8085 0.8046 0.8046 0.8014 0.8014 0.7476 0.7476 0.7159 0.7159 0.6988 0.6988 0.5805 0.5805 0.4744 0.3942 0.3942 0.2409
## Call:
## VAR(y = covid_reduced, p = 8, type = "const")
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -3.137e-03  5.164e-02  -0.061   0.9516    
## case_count.l1                  1.492e+00  5.776e-01   2.584   0.0101 *  
## vaccine_doses_administered.l1  4.256e-02  7.317e-02   0.582   0.5611    
## mobility_mean.l1               5.304e+02  4.544e+02   1.167   0.2438    
## tests_taken.l2                -3.610e-02  5.127e-02  -0.704   0.4818    
## case_count.l2                  8.663e-01  5.944e-01   1.457   0.1458    
## vaccine_doses_administered.l2 -2.517e-02  8.319e-02  -0.303   0.7624    
## mobility_mean.l2               3.190e+02  5.162e+02   0.618   0.5369    
## tests_taken.l3                -9.317e-02  5.091e-02  -1.830   0.0680 .  
## case_count.l3                  1.166e+00  5.829e-01   2.001   0.0461 *  
## vaccine_doses_administered.l3  5.742e-02  8.318e-02   0.690   0.4904    
## mobility_mean.l3               8.330e+01  5.154e+02   0.162   0.8717    
## tests_taken.l4                 1.012e-01  5.024e-02   2.015   0.0446 *  
## case_count.l4                 -8.671e-01  5.855e-01  -1.481   0.1395    
## vaccine_doses_administered.l4  4.444e-02  8.255e-02   0.538   0.5907    
## mobility_mean.l4               1.091e+02  5.162e+02   0.211   0.8328    
## tests_taken.l5                 6.750e-02  4.988e-02   1.353   0.1768    
## case_count.l5                  2.322e+00  5.840e-01   3.976 8.42e-05 ***
## vaccine_doses_administered.l5 -1.880e-02  8.292e-02  -0.227   0.8208    
## mobility_mean.l5               2.668e+02  5.143e+02   0.519   0.6043    
## tests_taken.l6                 1.100e-01  4.970e-02   2.213   0.0275 *  
## case_count.l6                  2.352e-01  5.956e-01   0.395   0.6932    
## vaccine_doses_administered.l6 -1.305e-01  8.346e-02  -1.564   0.1188    
## mobility_mean.l6              -9.257e+01  5.138e+02  -0.180   0.8571    
## tests_taken.l7                 1.043e-01  4.949e-02   2.107   0.0358 *  
## case_count.l7                 -3.631e-01  6.015e-01  -0.604   0.5465    
## vaccine_doses_administered.l7  1.118e-01  8.391e-02   1.332   0.1837    
## mobility_mean.l7              -3.719e+02  5.123e+02  -0.726   0.4684    
## tests_taken.l8                -6.073e-04  4.872e-02  -0.012   0.9901    
## case_count.l8                  3.622e-01  5.961e-01   0.608   0.5439    
## vaccine_doses_administered.l8 -3.348e-02  7.492e-02  -0.447   0.6553    
## mobility_mean.l8               1.587e+02  4.634e+02   0.343   0.7321    
## const                          4.214e+04  7.990e+03   5.274 2.26e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 33900 on 375 degrees of freedom
## Multiple R-Squared: 0.5073,  Adjusted R-squared: 0.4653 
## F-statistic: 12.07 on 32 and 375 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count: 
## =========================================== 
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.774e-03  4.612e-03   0.385 0.700656    
## case_count.l1                  3.618e-01  5.158e-02   7.013 1.09e-11 ***
## vaccine_doses_administered.l1  2.933e-02  6.534e-03   4.488 9.56e-06 ***
## mobility_mean.l1               1.197e+02  4.058e+01   2.951 0.003370 ** 
## tests_taken.l2                 7.240e-03  4.579e-03   1.581 0.114665    
## case_count.l2                 -1.162e-01  5.308e-02  -2.188 0.029254 *  
## vaccine_doses_administered.l2 -2.492e-02  7.429e-03  -3.355 0.000875 ***
## mobility_mean.l2              -4.252e+01  4.609e+01  -0.923 0.356847    
## tests_taken.l3                 9.642e-03  4.546e-03   2.121 0.034597 *  
## case_count.l3                  7.315e-02  5.205e-02   1.405 0.160757    
## vaccine_doses_administered.l3  8.238e-03  7.428e-03   1.109 0.268102    
## mobility_mean.l3              -2.112e+00  4.602e+01  -0.046 0.963424    
## tests_taken.l4                 1.905e-04  4.486e-03   0.042 0.966159    
## case_count.l4                  8.491e-02  5.229e-02   1.624 0.105220    
## vaccine_doses_administered.l4 -9.461e-03  7.372e-03  -1.283 0.200127    
## mobility_mean.l4              -1.035e+02  4.610e+01  -2.245 0.025377 *  
## tests_taken.l5                -2.349e-03  4.454e-03  -0.527 0.598219    
## case_count.l5                 -8.734e-02  5.215e-02  -1.675 0.094841 .  
## vaccine_doses_administered.l5  9.837e-03  7.404e-03   1.329 0.184816    
## mobility_mean.l5               2.678e+01  4.593e+01   0.583 0.560152    
## tests_taken.l6                -6.751e-03  4.438e-03  -1.521 0.129033    
## case_count.l6                  2.758e-01  5.319e-02   5.184 3.55e-07 ***
## vaccine_doses_administered.l6 -8.642e-03  7.453e-03  -1.160 0.246984    
## mobility_mean.l6               6.429e+01  4.589e+01   1.401 0.162013    
## tests_taken.l7                -9.700e-03  4.419e-03  -2.195 0.028780 *  
## case_count.l7                  3.075e-01  5.372e-02   5.724 2.13e-08 ***
## vaccine_doses_administered.l7 -2.975e-03  7.493e-03  -0.397 0.691593    
## mobility_mean.l7              -2.888e+01  4.575e+01  -0.631 0.528254    
## tests_taken.l8                -1.249e-03  4.351e-03  -0.287 0.774187    
## case_count.l8                  4.530e-02  5.323e-02   0.851 0.395383    
## vaccine_doses_administered.l8 -6.028e-03  6.691e-03  -0.901 0.368164    
## mobility_mean.l8              -2.616e+01  4.138e+01  -0.632 0.527708    
## const                          9.067e+02  7.135e+02   1.271 0.204603    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3027 on 375 degrees of freedom
## Multiple R-Squared: 0.7754,  Adjusted R-squared: 0.7562 
## F-statistic: 40.46 on 32 and 375 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -1.662e-02  3.048e-02  -0.545 0.585907    
## case_count.l1                 -6.721e-01  3.409e-01  -1.972 0.049381 *  
## vaccine_doses_administered.l1  8.276e-01  4.318e-02  19.165  < 2e-16 ***
## mobility_mean.l1               6.432e+01  2.682e+02   0.240 0.810554    
## tests_taken.l2                 7.574e-05  3.026e-02   0.003 0.998004    
## case_count.l2                  3.534e-01  3.508e-01   1.007 0.314364    
## vaccine_doses_administered.l2 -7.271e-02  4.909e-02  -1.481 0.139455    
## mobility_mean.l2               1.019e+03  3.046e+02   3.345 0.000907 ***
## tests_taken.l3                 3.699e-03  3.004e-02   0.123 0.902066    
## case_count.l3                 -2.823e-01  3.440e-01  -0.821 0.412306    
## vaccine_doses_administered.l3 -5.348e-02  4.909e-02  -1.089 0.276637    
## mobility_mean.l3              -5.471e+02  3.041e+02  -1.799 0.072864 .  
## tests_taken.l4                -2.309e-02  2.965e-02  -0.779 0.436577    
## case_count.l4                 -1.774e-01  3.455e-01  -0.513 0.608016    
## vaccine_doses_administered.l4  8.927e-02  4.872e-02   1.832 0.067674 .  
## mobility_mean.l4               4.063e+02  3.046e+02   1.334 0.183111    
## tests_taken.l5                 9.500e-03  2.944e-02   0.323 0.747060    
## case_count.l5                  1.560e-01  3.447e-01   0.453 0.651146    
## vaccine_doses_administered.l5 -1.011e-01  4.893e-02  -2.067 0.039448 *  
## mobility_mean.l5              -2.820e+02  3.035e+02  -0.929 0.353391    
## tests_taken.l6                -1.101e-03  2.933e-02  -0.038 0.970074    
## case_count.l6                 -3.010e-01  3.515e-01  -0.856 0.392351    
## vaccine_doses_administered.l6  1.475e-01  4.925e-02   2.995 0.002929 ** 
## mobility_mean.l6              -9.938e+01  3.032e+02  -0.328 0.743300    
## tests_taken.l7                 3.212e-02  2.920e-02   1.100 0.272187    
## case_count.l7                  6.726e-01  3.550e-01   1.895 0.058919 .  
## vaccine_doses_administered.l7  6.985e-01  4.952e-02  14.106  < 2e-16 ***
## mobility_mean.l7              -8.367e+02  3.023e+02  -2.767 0.005930 ** 
## tests_taken.l8                -1.684e-04  2.875e-02  -0.006 0.995331    
## case_count.l8                  7.902e-02  3.518e-01   0.225 0.822399    
## vaccine_doses_administered.l8 -5.657e-01  4.422e-02 -12.794  < 2e-16 ***
## mobility_mean.l8              -7.876e+01  2.735e+02  -0.288 0.773501    
## const                         -1.215e+02  4.715e+03  -0.026 0.979459    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 20000 on 375 degrees of freedom
## Multiple R-Squared: 0.9407,  Adjusted R-squared: 0.9357 
## F-statistic:   186 on 32 and 375 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 3.178e-06  5.728e-06   0.555 0.579372    
## case_count.l1                 -8.567e-05  6.407e-05  -1.337 0.181955    
## vaccine_doses_administered.l1  2.013e-05  8.116e-06   2.481 0.013543 *  
## mobility_mean.l1               6.107e-01  5.040e-02  12.119  < 2e-16 ***
## tests_taken.l2                -1.326e-06  5.687e-06  -0.233 0.815740    
## case_count.l2                 -5.911e-05  6.592e-05  -0.897 0.370450    
## vaccine_doses_administered.l2 -2.629e-05  9.227e-06  -2.849 0.004624 ** 
## mobility_mean.l2               1.196e-01  5.725e-02   2.089 0.037377 *  
## tests_taken.l3                 5.108e-06  5.647e-06   0.905 0.366277    
## case_count.l3                 -9.533e-05  6.465e-05  -1.475 0.141185    
## vaccine_doses_administered.l3  1.228e-05  9.226e-06   1.331 0.183997    
## mobility_mean.l3               1.028e-02  5.716e-02   0.180 0.857393    
## tests_taken.l4                -1.272e-05  5.572e-06  -2.282 0.023026 *  
## case_count.l4                  4.180e-05  6.494e-05   0.644 0.520144    
## vaccine_doses_administered.l4 -1.943e-05  9.156e-06  -2.122 0.034464 *  
## mobility_mean.l4               8.696e-02  5.725e-02   1.519 0.129670    
## tests_taken.l5                -3.722e-06  5.532e-06  -0.673 0.501498    
## case_count.l5                  2.191e-05  6.477e-05   0.338 0.735418    
## vaccine_doses_administered.l5  1.814e-05  9.196e-06   1.972 0.049335 *  
## mobility_mean.l5              -1.084e-01  5.704e-02  -1.900 0.058167 .  
## tests_taken.l6                 2.740e-06  5.512e-06   0.497 0.619356    
## case_count.l6                 -1.102e-04  6.606e-05  -1.669 0.096045 .  
## vaccine_doses_administered.l6 -6.472e-06  9.257e-06  -0.699 0.484907    
## mobility_mean.l6               7.966e-02  5.699e-02   1.398 0.163019    
## tests_taken.l7                -1.282e-06  5.489e-06  -0.234 0.815400    
## case_count.l7                  9.192e-05  6.672e-05   1.378 0.169084    
## vaccine_doses_administered.l7 -1.842e-05  9.306e-06  -1.979 0.048551 *  
## mobility_mean.l7               2.692e-01  5.682e-02   4.738 3.07e-06 ***
## tests_taken.l8                 4.387e-06  5.404e-06   0.812 0.417440    
## case_count.l8                  1.171e-04  6.612e-05   1.770 0.077463 .  
## vaccine_doses_administered.l8  2.016e-05  8.310e-06   2.426 0.015721 *  
## mobility_mean.l8              -1.970e-01  5.139e-02  -3.833 0.000148 ***
## const                         -3.717e-01  8.862e-01  -0.419 0.675169    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.76 on 375 degrees of freedom
## Multiple R-Squared: 0.7433,  Adjusted R-squared: 0.7214 
## F-statistic: 33.93 on 32 and 375 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                 1148992753  1679248.8                   25719223
## case_count                     1679249  9163047.4                    4474245
## vaccine_doses_administered    25719223  4474245.1                  400159322
## mobility_mean                    -1283      843.3                      16233
##                            mobility_mean
## tests_taken                     -1283.34
## case_count                        843.29
## vaccine_doses_administered      16232.89
## mobility_mean                      14.13
## 
## Correlation matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                    1.00000    0.01637                    0.03793
## case_count                     0.01637    1.00000                    0.07389
## vaccine_doses_administered     0.03793    0.07389                    1.00000
## mobility_mean                 -0.01007    0.07410                    0.21584
##                            mobility_mean
## tests_taken                     -0.01007
## case_count                       0.07410
## vaccine_doses_administered       0.21584
## mobility_mean                    1.00000

preds=predict(fit1a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l")
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit1a = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit1a

## [1] 3110599

short_ASE_fit1a^.5

## [1] 1763.689

#7 Day RMSE of 1763.7 which is much lower than the 2981 from our ARIMA(6,1,14) model
#Maybe try to look up rolling window version

long_ASE_fit1a = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit1a

## [1] 1759871

long_ASE_fit1a^.5

## [1] 1326.601

#RMSE of 1326.6 which is much lower than the 3806 from our ARIMA(6,1,14) model
#Maybe try to look up rolling window version

#Fit based on BIC
#Same

#Test just a seasonal data set
VARselect(covid_reduced,lag.max = 25,type = 'const',season = 7)

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      8      8      2      8 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.060979e+01 6.040078e+01 6.028869e+01 6.019487e+01 6.010890e+01
## HQ(n)  6.078681e+01 6.064217e+01 6.059445e+01 6.056500e+01 6.054341e+01
## SC(n)  6.105640e+01 6.100979e+01 6.106010e+01 6.112868e+01 6.120512e+01
## FPE(n) 2.101473e+26 1.705257e+26 1.524673e+26 1.388464e+26 1.274524e+26
##                   6            7            8            9           10
## AIC(n) 5.978701e+01 5.970747e+01 5.947442e+01 5.949180e+01 5.951194e+01
## HQ(n)  6.028589e+01 6.027072e+01 6.010203e+01 6.018379e+01 6.026830e+01
## SC(n)  6.104563e+01 6.112849e+01 6.105784e+01 6.123763e+01 6.142017e+01
## FPE(n) 9.241645e+25 8.540049e+25 6.769682e+25 6.894675e+25 7.042658e+25
##                  11           12           13           14           15
## AIC(n) 5.954056e+01 5.954482e+01 5.957640e+01 5.960675e+01 5.960202e+01
## HQ(n)  6.036128e+01 6.042992e+01 6.052587e+01 6.062059e+01 6.068023e+01
## SC(n)  6.161119e+01 6.177786e+01 6.197184e+01 6.216459e+01 6.232226e+01
## FPE(n) 7.256565e+25 7.298778e+25 7.546337e+25 7.794777e+25 7.776078e+25
##                  16           17           18           19           20
## AIC(n) 5.963388e+01 5.964254e+01 5.966629e+01 5.970882e+01 5.969266e+01
## HQ(n)  6.077647e+01 6.084949e+01 6.093761e+01 6.104451e+01 6.109273e+01
## SC(n)  6.251653e+01 6.268758e+01 6.287373e+01 6.307866e+01 6.322491e+01
## FPE(n) 8.048998e+25 8.143003e+25 8.366270e+25 8.761863e+25 8.656536e+25
##                  21           22           23           24           25
## AIC(n) 5.973521e+01 5.970227e+01 5.971505e+01 5.975114e+01 5.979909e+01
## HQ(n)  6.119965e+01 6.123107e+01 6.130823e+01 6.140868e+01 6.152101e+01
## SC(n)  6.342987e+01 6.355932e+01 6.373451e+01 6.393300e+01 6.414335e+01
## FPE(n) 9.073343e+25 8.822468e+25 8.984112e+25 9.368864e+25 9.891819e+25

  #AIC 8, BIC 2

#Fit based on AIC
fit2a=VAR(covid_reduced,p=8,type="const",season = 7)
summary(fit2a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean 
## Deterministic variables: const 
## Sample size: 408 
## Log Likelihood: -14281.152 
## Roots of the characteristic polynomial:
## 0.9892 0.9892 0.9737 0.9737 0.9485 0.9485 0.9186 0.8907 0.8907 0.8787 0.8787 0.8424 0.8424 0.839 0.793 0.793 0.7566 0.7566 0.7383 0.7383 0.738 0.738 0.6698 0.6567 0.6567 0.6407 0.6407 0.6215 0.6215 0.6105 0.6105 0.03927
## Call:
## VAR(y = covid_reduced, p = 8, type = "const", season = 7L)
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -1.286e-03  5.207e-02  -0.025   0.9803    
## case_count.l1                  1.406e+00  6.105e-01   2.303   0.0219 *  
## vaccine_doses_administered.l1  7.124e-02  8.116e-02   0.878   0.3806    
## mobility_mean.l1               3.037e+02  4.949e+02   0.614   0.5397    
## tests_taken.l2                -3.312e-02  5.176e-02  -0.640   0.5226    
## case_count.l2                  6.297e-01  6.309e-01   0.998   0.3189    
## vaccine_doses_administered.l2 -8.621e-02  1.009e-01  -0.854   0.3934    
## mobility_mean.l2               5.465e+02  6.029e+02   0.906   0.3653    
## tests_taken.l3                -9.207e-02  5.149e-02  -1.788   0.0746 .  
## case_count.l3                  1.189e+00  6.187e-01   1.922   0.0554 .  
## vaccine_doses_administered.l3  8.163e-02  1.001e-01   0.816   0.4151    
## mobility_mean.l3               2.638e+02  6.058e+02   0.435   0.6635    
## tests_taken.l4                 1.065e-01  5.116e-02   2.081   0.0381 *  
## case_count.l4                 -6.649e-01  6.238e-01  -1.066   0.2871    
## vaccine_doses_administered.l4  3.390e-02  9.956e-02   0.340   0.7337    
## mobility_mean.l4               1.018e+02  6.064e+02   0.168   0.8668    
## tests_taken.l5                 7.150e-02  5.076e-02   1.409   0.1598    
## case_count.l5                  2.469e+00  6.218e-01   3.970 8.64e-05 ***
## vaccine_doses_administered.l5  3.676e-02  9.988e-02   0.368   0.7131    
## mobility_mean.l5               3.655e+01  6.044e+02   0.060   0.9518    
## tests_taken.l6                 1.121e-01  5.061e-02   2.214   0.0274 *  
## case_count.l6                  1.062e-01  6.305e-01   0.168   0.8663    
## vaccine_doses_administered.l6 -1.647e-01  1.005e-01  -1.639   0.1020    
## mobility_mean.l6              -2.214e+02  6.021e+02  -0.368   0.7133    
## tests_taken.l7                 9.479e-02  5.045e-02   1.879   0.0611 .  
## case_count.l7                 -2.385e-01  6.326e-01  -0.377   0.7064    
## vaccine_doses_administered.l7  8.254e-02  1.019e-01   0.810   0.4183    
## mobility_mean.l7              -1.385e+01  6.003e+02  -0.023   0.9816    
## tests_taken.l8                -3.639e-03  4.978e-02  -0.073   0.9418    
## case_count.l8                  2.585e-01  6.070e-01   0.426   0.6705    
## vaccine_doses_administered.l8 -7.832e-03  8.261e-02  -0.095   0.9245    
## mobility_mean.l8              -4.741e+01  5.164e+02  -0.092   0.9269    
## const                          4.185e+04  8.026e+03   5.214 3.08e-07 ***
## sd1                            8.388e+02  1.114e+04   0.075   0.9400    
## sd2                           -7.518e+03  1.259e+04  -0.597   0.5509    
## sd3                            3.743e+01  1.078e+04   0.003   0.9972    
## sd4                            4.356e+03  1.073e+04   0.406   0.6850    
## sd5                            9.403e+03  1.256e+04   0.749   0.4545    
## sd6                           -7.825e+03  1.140e+04  -0.686   0.4931    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 34010 on 369 degrees of freedom
## Multiple R-Squared: 0.512,   Adjusted R-squared: 0.4618 
## F-statistic: 10.19 on 38 and 369 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count: 
## =========================================== 
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.235e-03  4.390e-03   0.281 0.778661    
## case_count.l1                  3.400e-01  5.146e-02   6.607 1.37e-10 ***
## vaccine_doses_administered.l1  1.524e-02  6.842e-03   2.228 0.026506 *  
## mobility_mean.l1               2.130e+02  4.172e+01   5.107 5.27e-07 ***
## tests_taken.l2                 8.413e-03  4.363e-03   1.928 0.054585 .  
## case_count.l2                 -5.779e-02  5.319e-02  -1.087 0.277928    
## vaccine_doses_administered.l2 -7.426e-03  8.505e-03  -0.873 0.383109    
## mobility_mean.l2              -9.565e+01  5.083e+01  -1.882 0.060643 .  
## tests_taken.l3                 1.230e-02  4.341e-03   2.833 0.004861 ** 
## case_count.l3                  9.092e-02  5.216e-02   1.743 0.082145 .  
## vaccine_doses_administered.l3  1.184e-02  8.434e-03   1.404 0.161255    
## mobility_mean.l3              -4.930e+01  5.107e+01  -0.965 0.334961    
## tests_taken.l4                 7.756e-04  4.313e-03   0.180 0.857385    
## case_count.l4                  1.178e-01  5.258e-02   2.240 0.025653 *  
## vaccine_doses_administered.l4 -1.221e-02  8.392e-03  -1.455 0.146419    
## mobility_mean.l4              -9.871e+01  5.112e+01  -1.931 0.054273 .  
## tests_taken.l5                -3.491e-03  4.279e-03  -0.816 0.415055    
## case_count.l5                 -3.462e-02  5.242e-02  -0.660 0.509360    
## vaccine_doses_administered.l5  5.389e-03  8.419e-03   0.640 0.522507    
## mobility_mean.l5               2.474e+01  5.095e+01   0.486 0.627510    
## tests_taken.l6                -6.714e-03  4.267e-03  -1.574 0.116406    
## case_count.l6                  2.537e-01  5.315e-02   4.773 2.62e-06 ***
## vaccine_doses_administered.l6  2.364e-03  8.469e-03   0.279 0.780314    
## mobility_mean.l6              -1.929e+01  5.075e+01  -0.380 0.704100    
## tests_taken.l7                -9.989e-03  4.253e-03  -2.349 0.019372 *  
## case_count.l7                  1.961e-01  5.333e-02   3.677 0.000271 ***
## vaccine_doses_administered.l7 -1.630e-02  8.587e-03  -1.898 0.058429 .  
## mobility_mean.l7              -2.859e+01  5.061e+01  -0.565 0.572412    
## tests_taken.l8                -3.717e-03  4.196e-03  -0.886 0.376326    
## case_count.l8                  4.592e-02  5.117e-02   0.897 0.370140    
## vaccine_doses_administered.l8 -3.096e-03  6.964e-03  -0.445 0.656931    
## mobility_mean.l8               7.231e+01  4.353e+01   1.661 0.097495 .  
## const                          9.233e+02  6.765e+02   1.365 0.173142    
## sd1                            2.530e+03  9.391e+02   2.695 0.007369 ** 
## sd2                            6.526e+03  1.062e+03   6.148 2.04e-09 ***
## sd3                            5.293e+03  9.088e+02   5.824 1.25e-08 ***
## sd4                            3.452e+03  9.043e+02   3.817 0.000158 ***
## sd5                            3.993e+03  1.059e+03   3.772 0.000189 ***
## sd6                            4.626e+03  9.613e+02   4.813 2.18e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 2867 on 369 degrees of freedom
## Multiple R-Squared: 0.8018,  Adjusted R-squared: 0.7814 
## F-statistic: 39.28 on 38 and 369 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -1.859e-02  2.986e-02  -0.622  0.53409    
## case_count.l1                 -5.233e-01  3.501e-01  -1.494  0.13593    
## vaccine_doses_administered.l1  8.641e-01  4.655e-02  18.564  < 2e-16 ***
## mobility_mean.l1               1.360e+02  2.838e+02   0.479  0.63214    
## tests_taken.l2                 1.568e-02  2.968e-02   0.528  0.59773    
## case_count.l2                  1.304e-01  3.619e-01   0.360  0.71871    
## vaccine_doses_administered.l2 -1.053e-01  5.786e-02  -1.819  0.06974 .  
## mobility_mean.l2               6.902e+02  3.458e+02   1.996  0.04669 *  
## tests_taken.l3                 1.537e-03  2.953e-02   0.052  0.95852    
## case_count.l3                 -5.666e-02  3.549e-01  -0.160  0.87323    
## vaccine_doses_administered.l3 -6.816e-02  5.739e-02  -1.188  0.23570    
## mobility_mean.l3              -1.644e+01  3.474e+02  -0.047  0.96228    
## tests_taken.l4                -2.290e-02  2.934e-02  -0.780  0.43568    
## case_count.l4                  6.357e-02  3.578e-01   0.178  0.85907    
## vaccine_doses_administered.l4  1.358e-01  5.710e-02   2.377  0.01794 *  
## mobility_mean.l4              -4.604e+00  3.478e+02  -0.013  0.98945    
## tests_taken.l5                 1.641e-02  2.911e-02   0.564  0.57344    
## case_count.l5                  2.202e-01  3.566e-01   0.617  0.53740    
## vaccine_doses_administered.l5 -1.290e-01  5.729e-02  -2.253  0.02487 *  
## mobility_mean.l5              -3.442e+02  3.466e+02  -0.993  0.32141    
## tests_taken.l6                -1.055e-02  2.903e-02  -0.363  0.71659    
## case_count.l6                 -6.214e-01  3.616e-01  -1.718  0.08656 .  
## vaccine_doses_administered.l6  1.894e-01  5.762e-02   3.288  0.00111 ** 
## mobility_mean.l6              -3.471e+02  3.453e+02  -1.005  0.31542    
## tests_taken.l7                 2.781e-02  2.894e-02   0.961  0.33714    
## case_count.l7                  5.334e-01  3.628e-01   1.470  0.14237    
## vaccine_doses_administered.l7  5.655e-01  5.842e-02   9.680  < 2e-16 ***
## mobility_mean.l7              -2.596e+02  3.443e+02  -0.754  0.45128    
## tests_taken.l8                -8.422e-03  2.855e-02  -0.295  0.76817    
## case_count.l8                  1.124e-01  3.482e-01   0.323  0.74698    
## vaccine_doses_administered.l8 -4.795e-01  4.738e-02 -10.118  < 2e-16 ***
## mobility_mean.l8              -1.992e+02  2.962e+02  -0.673  0.50156    
## const                         -1.523e+02  4.603e+03  -0.033  0.97363    
## sd1                            2.679e+04  6.389e+03   4.193 3.45e-05 ***
## sd2                            8.533e+03  7.223e+03   1.181  0.23821    
## sd3                            1.639e+04  6.184e+03   2.650  0.00839 ** 
## sd4                            1.796e+04  6.153e+03   2.919  0.00373 ** 
## sd5                            1.698e+04  7.202e+03   2.357  0.01894 *  
## sd6                            5.478e+03  6.541e+03   0.838  0.40283    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 19510 on 369 degrees of freedom
## Multiple R-Squared: 0.9446,  Adjusted R-squared: 0.9389 
## F-statistic: 165.4 on 38 and 369 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.937e-06  5.577e-06   0.347 0.728609    
## case_count.l1                 -1.307e-04  6.539e-05  -1.998 0.046398 *  
## vaccine_doses_administered.l1  7.439e-06  8.693e-06   0.856 0.392660    
## mobility_mean.l1               6.660e-01  5.300e-02  12.565  < 2e-16 ***
## tests_taken.l2                -2.298e-06  5.543e-06  -0.414 0.678783    
## case_count.l2                 -2.749e-05  6.758e-05  -0.407 0.684422    
## vaccine_doses_administered.l2 -1.243e-05  1.081e-05  -1.150 0.250898    
## mobility_mean.l2               1.060e-01  6.458e-02   1.642 0.101521    
## tests_taken.l3                 5.824e-06  5.515e-06   1.056 0.291639    
## case_count.l3                 -1.003e-04  6.627e-05  -1.513 0.131078    
## vaccine_doses_administered.l3  8.217e-06  1.072e-05   0.767 0.443702    
## mobility_mean.l3              -1.331e-02  6.488e-02  -0.205 0.837616    
## tests_taken.l4                -1.148e-05  5.480e-06  -2.095 0.036813 *  
## case_count.l4                  2.033e-05  6.681e-05   0.304 0.761104    
## vaccine_doses_administered.l4 -8.784e-06  1.066e-05  -0.824 0.410585    
## mobility_mean.l4               6.763e-02  6.495e-02   1.041 0.298480    
## tests_taken.l5                -3.308e-06  5.437e-06  -0.608 0.543230    
## case_count.l5                  3.920e-05  6.660e-05   0.589 0.556519    
## vaccine_doses_administered.l5  8.460e-07  1.070e-05   0.079 0.937008    
## mobility_mean.l5              -5.149e-02  6.473e-02  -0.795 0.426901    
## tests_taken.l6                 1.917e-06  5.421e-06   0.354 0.723866    
## case_count.l6                 -1.843e-05  6.753e-05  -0.273 0.785096    
## vaccine_doses_administered.l6  7.248e-06  1.076e-05   0.674 0.501008    
## mobility_mean.l6               7.490e-02  6.448e-02   1.162 0.246183    
## tests_taken.l7                 1.013e-06  5.404e-06   0.188 0.851352    
## case_count.l7                  3.703e-05  6.776e-05   0.546 0.585069    
## vaccine_doses_administered.l7 -9.222e-06  1.091e-05  -0.845 0.398499    
## mobility_mean.l7               1.058e-01  6.430e-02   1.646 0.100656    
## tests_taken.l8                 2.992e-06  5.332e-06   0.561 0.574975    
## case_count.l8                  1.035e-04  6.502e-05   1.592 0.112188    
## vaccine_doses_administered.l8  6.353e-06  8.849e-06   0.718 0.473253    
## mobility_mean.l8              -7.723e-02  5.530e-02  -1.396 0.163424    
## const                         -2.965e-01  8.596e-01  -0.345 0.730365    
## sd1                           -2.067e+00  1.193e+00  -1.733 0.083994 .  
## sd2                            1.366e+00  1.349e+00   1.013 0.311946    
## sd3                            1.504e+00  1.155e+00   1.303 0.193508    
## sd4                            9.989e-01  1.149e+00   0.869 0.385198    
## sd5                           -1.038e+00  1.345e+00  -0.772 0.440728    
## sd6                            4.286e+00  1.221e+00   3.509 0.000505 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.642 on 369 degrees of freedom
## Multiple R-Squared: 0.7629,  Adjusted R-squared: 0.7384 
## F-statistic: 31.24 on 38 and 369 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                  1.157e+09  2708450.0                   19760118
## case_count                   2.708e+06  8218347.5                    2961014
## vaccine_doses_administered   1.976e+07  2961013.7                  380451997
## mobility_mean                9.343e+02      406.1                      18685
##                            mobility_mean
## tests_taken                       934.32
## case_count                        406.13
## vaccine_doses_administered      18684.52
## mobility_mean                      13.27
## 
## Correlation matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                   1.000000    0.02778                    0.02979
## case_count                    0.027781    1.00000                    0.05295
## vaccine_doses_administered    0.029789    0.05295                    1.00000
## mobility_mean                 0.007543    0.03889                    0.26299
##                            mobility_mean
## tests_taken                     0.007543
## case_count                      0.038894
## vaccine_doses_administered      0.262991
## mobility_mean                   1.000000

preds=predict(fit2a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l",ylim=c(400,5900))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit2a = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit2a

## [1] 4269497

short_ASE_fit2a^.5

## [1] 2066.276

#7 Day RMSE of 2066.2 which is much lower than the 2981 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version

long_ASE_fit2a = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit2a

## [1] 2316924

long_ASE_fit2a^.5

## [1] 1522.145

#21 Day RMSE of 1522.145 which is much lower than the 3806 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version

#Fit based on BIC
fit2b=VAR(covid_reduced,p=2,type="const",season = 7)
summary(fit2b)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean 
## Deterministic variables: const 
## Sample size: 414 
## Log Likelihood: -14786.812 
## Roots of the characteristic polynomial:
## 0.9374 0.8802 0.7942 0.4141 0.4141 0.3528 0.1909 0.1645
## Call:
## VAR(y = covid_reduced, p = 2, type = "const", season = 7L)
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.061e-01  4.883e-02   2.174   0.0303 *  
## case_count.l1                  2.270e+00  5.045e-01   4.500 8.93e-06 ***
## vaccine_doses_administered.l1  6.495e-02  6.348e-02   1.023   0.3068    
## mobility_mean.l1               4.125e+02  4.950e+02   0.833   0.4051    
## tests_taken.l2                 8.290e-02  4.689e-02   1.768   0.0778 .  
## case_count.l2                  2.291e+00  5.410e-01   4.235 2.84e-05 ***
## vaccine_doses_administered.l2 -2.308e-03  6.375e-02  -0.036   0.9711    
## mobility_mean.l2              -8.240e+01  4.859e+02  -0.170   0.8654    
## const                          4.459e+04  5.699e+03   7.825 4.59e-14 ***
## sd1                            1.255e+04  7.643e+03   1.642   0.1013    
## sd2                            6.541e+03  9.897e+03   0.661   0.5091    
## sd3                           -4.083e+03  7.999e+03  -0.511   0.6100    
## sd4                           -1.095e+03  7.556e+03  -0.145   0.8848    
## sd5                            7.534e+03  7.554e+03   0.997   0.3192    
## sd6                           -7.319e+03  8.238e+03  -0.888   0.3748    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35850 on 399 degrees of freedom
## Multiple R-Squared: 0.4222,  Adjusted R-squared: 0.402 
## F-statistic: 20.83 on 14 and 399 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count: 
## =========================================== 
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.261e-02  4.546e-03   2.774  0.00579 ** 
## case_count.l1                  6.176e-01  4.697e-02  13.148  < 2e-16 ***
## vaccine_doses_administered.l1  2.862e-03  5.910e-03   0.484  0.62847    
## mobility_mean.l1               1.975e+02  4.608e+01   4.285 2.29e-05 ***
## tests_taken.l2                 1.950e-02  4.366e-03   4.467 1.03e-05 ***
## case_count.l2                  2.948e-02  5.037e-02   0.585  0.55864    
## vaccine_doses_administered.l2 -7.114e-03  5.935e-03  -1.199  0.23138    
## mobility_mean.l2              -2.479e+02  4.524e+01  -5.480 7.55e-08 ***
## const                         -8.120e+02  5.305e+02  -1.530  0.12670    
## sd1                            4.596e+03  7.115e+02   6.459 3.06e-10 ***
## sd2                            8.193e+03  9.214e+02   8.892  < 2e-16 ***
## sd3                            4.452e+03  7.447e+02   5.978 5.02e-09 ***
## sd4                            3.384e+03  7.034e+02   4.810 2.14e-06 ***
## sd5                            4.302e+03  7.033e+02   6.117 2.28e-09 ***
## sd6                            4.700e+03  7.669e+02   6.128 2.14e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3337 on 399 degrees of freedom
## Multiple R-Squared: 0.7107,  Adjusted R-squared: 0.7005 
## F-statistic:    70 on 14 and 399 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -6.314e-02  3.816e-02  -1.654   0.0988 .  
## case_count.l1                 -2.940e-01  3.943e-01  -0.746   0.4564    
## vaccine_doses_administered.l1  1.108e+00  4.961e-02  22.340  < 2e-16 ***
## mobility_mean.l1              -2.160e+02  3.869e+02  -0.558   0.5769    
## tests_taken.l2                 7.185e-02  3.665e-02   1.961   0.0506 .  
## case_count.l2                  1.204e-01  4.228e-01   0.285   0.7760    
## vaccine_doses_administered.l2 -2.002e-01  4.982e-02  -4.017 7.03e-05 ***
## mobility_mean.l2               2.564e+02  3.798e+02   0.675   0.5000    
## const                          8.364e+03  4.454e+03   1.878   0.0611 .  
## sd1                            7.548e+04  5.973e+03  12.637  < 2e-16 ***
## sd2                            3.465e+04  7.735e+03   4.480 9.78e-06 ***
## sd3                            3.712e+04  6.252e+03   5.937 6.31e-09 ***
## sd4                            3.332e+04  5.905e+03   5.642 3.19e-08 ***
## sd5                            3.658e+04  5.904e+03   6.196 1.45e-09 ***
## sd6                           -7.904e+03  6.438e+03  -1.228   0.2203    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 28020 on 399 degrees of freedom
## Multiple R-Squared: 0.8783,  Adjusted R-squared: 0.874 
## F-statistic: 205.6 on 14 and 399 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 4.762e-06  4.978e-06   0.957 0.339344    
## case_count.l1                 -1.095e-04  5.144e-05  -2.129 0.033852 *  
## vaccine_doses_administered.l1  3.571e-06  6.472e-06   0.552 0.581379    
## mobility_mean.l1               6.905e-01  5.046e-02  13.682  < 2e-16 ***
## tests_taken.l2                 1.959e-06  4.781e-06   0.410 0.682227    
## case_count.l2                 -7.118e-05  5.515e-05  -1.291 0.197606    
## vaccine_doses_administered.l2 -4.228e-06  6.499e-06  -0.651 0.515734    
## mobility_mean.l2               1.282e-01  4.954e-02   2.589 0.009980 ** 
## const                         -1.152e+00  5.810e-01  -1.983 0.048066 *  
## sd1                           -2.951e+00  7.792e-01  -3.787 0.000176 ***
## sd2                            1.134e+00  1.009e+00   1.124 0.261740    
## sd3                            2.597e+00  8.155e-01   3.184 0.001564 ** 
## sd4                            2.020e+00  7.703e-01   2.623 0.009059 ** 
## sd5                           -1.612e+00  7.702e-01  -2.093 0.037008 *  
## sd6                            4.883e+00  8.399e-01   5.814 1.25e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.655 on 399 degrees of freedom
## Multiple R-Squared: 0.7435,  Adjusted R-squared: 0.7345 
## F-statistic:  82.6 on 14 and 399 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                 1284949096  7335889.6                  -25228520
## case_count                     7335890 11137605.8                   -7740908
## vaccine_doses_administered   -25228520 -7740908.5                  784939569
## mobility_mean                     1592      291.8                      17647
##                            mobility_mean
## tests_taken                      1591.92
## case_count                        291.84
## vaccine_doses_administered      17647.35
## mobility_mean                      13.36
## 
## Correlation matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                    1.00000    0.06132                   -0.02512
## case_count                     0.06132    1.00000                   -0.08279
## vaccine_doses_administered    -0.02512   -0.08279                    1.00000
## mobility_mean                  0.01215    0.02393                    0.17235
##                            mobility_mean
## tests_taken                      0.01215
## case_count                       0.02393
## vaccine_doses_administered       0.17235
## mobility_mean                    1.00000

preds=predict(fit2b,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l",ylim=c(400,5900))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit2b = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit2b

## [1] 2546313

short_ASE_fit2b^.5

## [1] 1595.717

#7 Day RMSE of 1595.7 which is much lower than the 2981 from our ARIMA(6,1,14) model and higher than fit 1a
#Maybe try to look up rolling window version

long_ASE_fit2b = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit2b

## [1] 6947698

long_ASE_fit2b^.5

## [1] 2635.849

#21 Day RMSE of 2635.8 which is much lower than the 3806 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version

#Test a first differenced data set
VARselect(covid_d1,lag.max = 25,type = 'const')

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      7      7      7      7 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.218100e+01 6.174680e+01 6.143869e+01 6.130257e+01 6.049874e+01
## HQ(n)  6.226163e+01 6.189193e+01 6.164832e+01 6.157670e+01 6.083737e+01
## SC(n)  6.238440e+01 6.211291e+01 6.196751e+01 6.199411e+01 6.135299e+01
## FPE(n) 1.011275e+27 6.551032e+26 4.814222e+26 4.202097e+26 1.881270e+26
##                   6            7            8            9           10
## AIC(n) 6.014111e+01 5.975010e+01 5.975529e+01 5.975026e+01 5.976555e+01
## HQ(n)  6.054424e+01 6.021773e+01 6.028742e+01 6.034689e+01 6.042668e+01
## SC(n)  6.115807e+01 6.092977e+01 6.109768e+01 6.125536e+01 6.143337e+01
## FPE(n) 1.316004e+26 8.904607e+25 8.955637e+25 8.916648e+25 9.061565e+25
##                  11           12           13           14           15
## AIC(n) 5.979913e+01 5.981682e+01 5.982840e+01 5.978511e+01 5.981326e+01
## HQ(n)  6.052476e+01 6.060696e+01 6.068303e+01 6.070425e+01 6.079690e+01
## SC(n)  6.162965e+01 6.181007e+01 6.198436e+01 6.210378e+01 6.229465e+01
## FPE(n) 9.380451e+25 9.559516e+25 9.684646e+25 9.289814e+25 9.573416e+25
##                  16           17           18           19           20
## AIC(n) 5.980962e+01 5.983894e+01 5.987629e+01 5.988328e+01 5.991005e+01
## HQ(n)  6.085775e+01 6.095158e+01 6.105343e+01 6.112492e+01 6.121618e+01
## SC(n)  6.245371e+01 6.264576e+01 6.284582e+01 6.301552e+01 6.320500e+01
## FPE(n) 9.559579e+25 9.868698e+25 1.027312e+26 1.037782e+26 1.069684e+26
##                  21           22           23           24           25
## AIC(n) 5.984962e+01 5.986197e+01 5.991650e+01 5.997629e+01 5.998206e+01
## HQ(n)  6.122026e+01 6.129711e+01 6.141614e+01 6.154043e+01 6.161070e+01
## SC(n)  6.330729e+01 6.348235e+01 6.369959e+01 6.392210e+01 6.409059e+01
## FPE(n) 1.010889e+26 1.027858e+26 1.090607e+26 1.163809e+26 1.177185e+26

  #AIC 7, BIC 7

#Fit based on AIC
fit3a=VAR(covid_d1,p=7,type="const")
summary(fit3a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean 
## Deterministic variables: const 
## Sample size: 408 
## Log Likelihood: -14376.36 
## Roots of the characteristic polynomial:
## 0.9871 0.9871 0.9839 0.9839 0.9472 0.9472 0.9275 0.9275 0.905 0.905 0.8003 0.8003 0.7986 0.7986 0.7956 0.7956 0.7355 0.7355 0.7053 0.7053 0.6303 0.6303 0.5913 0.5794 0.5794 0.5001 0.2447 0.133
## Call:
## VAR(y = covid_d1, p = 7, type = "const")
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                  -0.90447    0.05129 -17.634  < 2e-16 ***
## case_count.l1                    1.48701    0.59758   2.488  0.01326 *  
## vaccine_doses_administered.l1    0.06037    0.07560   0.799  0.42504    
## mobility_mean.l1               423.80902  467.77508   0.906  0.36551    
## tests_taken.l2                  -0.83550    0.06781 -12.320  < 2e-16 ***
## case_count.l2                    1.90671    0.67209   2.837  0.00480 ** 
## vaccine_doses_administered.l2    0.04006    0.07768   0.516  0.60634    
## mobility_mean.l2               541.58287  491.15846   1.103  0.27087    
## tests_taken.l3                  -0.81429    0.07644 -10.653  < 2e-16 ***
## case_count.l3                    2.29467    0.70474   3.256  0.00123 ** 
## vaccine_doses_administered.l3    0.08583    0.07563   1.135  0.25714    
## mobility_mean.l3               565.58403  503.73724   1.123  0.26224    
## tests_taken.l4                  -0.60045    0.08260  -7.269 2.09e-12 ***
## case_count.l4                    0.61988    0.72958   0.850  0.39606    
## vaccine_doses_administered.l4    0.12798    0.07851   1.630  0.10390    
## mobility_mean.l4               603.77284  511.44652   1.181  0.23853    
## tests_taken.l5                  -0.42061    0.07733  -5.439 9.63e-08 ***
## case_count.l5                    2.27264    0.68974   3.295  0.00108 ** 
## vaccine_doses_administered.l5    0.09277    0.07654   1.212  0.22627    
## mobility_mean.l5               718.53244  512.61627   1.402  0.16182    
## tests_taken.l6                  -0.21499    0.06715  -3.202  0.00148 ** 
## case_count.l6                    1.64501    0.67278   2.445  0.01494 *  
## vaccine_doses_administered.l6   -0.03959    0.07755  -0.511  0.60996    
## mobility_mean.l6               494.73207  506.21445   0.977  0.32904    
## tests_taken.l7                  -0.04047    0.04994  -0.810  0.41826    
## case_count.l7                    0.61948    0.59887   1.034  0.30160    
## vaccine_doses_administered.l7    0.07038    0.07721   0.911  0.36262    
## mobility_mean.l7                22.31164  477.72695   0.047  0.96277    
## const                           46.04632 1754.01731   0.026  0.97907    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35400 on 379 degrees of freedom
## Multiple R-Squared: 0.5179,  Adjusted R-squared: 0.4822 
## F-statistic: 14.54 on 28 and 379 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count: 
## =========================================== 
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.940e-03  4.404e-03   0.440  0.65987    
## case_count.l1                 -6.199e-01  5.130e-02 -12.082  < 2e-16 ***
## vaccine_doses_administered.l1  2.867e-02  6.490e-03   4.418 1.30e-05 ***
## mobility_mean.l1               1.233e+02  4.016e+01   3.071  0.00229 ** 
## tests_taken.l2                 9.386e-03  5.822e-03   1.612  0.10778    
## case_count.l2                 -7.281e-01  5.770e-02 -12.618  < 2e-16 ***
## vaccine_doses_administered.l2  3.664e-03  6.669e-03   0.549  0.58304    
## mobility_mean.l2               7.881e+01  4.217e+01   1.869  0.06242 .  
## tests_taken.l3                 1.910e-02  6.563e-03   2.911  0.00381 ** 
## case_count.l3                 -6.465e-01  6.051e-02 -10.685  < 2e-16 ***
## vaccine_doses_administered.l3  1.282e-02  6.493e-03   1.974  0.04912 *  
## mobility_mean.l3               7.598e+01  4.325e+01   1.757  0.07974 .  
## tests_taken.l4                 1.922e-02  7.092e-03   2.710  0.00704 ** 
## case_count.l4                 -5.534e-01  6.264e-02  -8.835  < 2e-16 ***
## vaccine_doses_administered.l4  3.782e-03  6.740e-03   0.561  0.57506    
## mobility_mean.l4              -2.795e+01  4.391e+01  -0.637  0.52476    
## tests_taken.l5                 1.694e-02  6.639e-03   2.551  0.01113 *  
## case_count.l5                 -6.349e-01  5.922e-02 -10.722  < 2e-16 ***
## vaccine_doses_administered.l5  1.451e-02  6.572e-03   2.208  0.02783 *  
## mobility_mean.l5              -2.274e+00  4.401e+01  -0.052  0.95882    
## tests_taken.l6                 1.034e-02  5.765e-03   1.794  0.07366 .  
## case_count.l6                 -3.504e-01  5.776e-02  -6.066 3.18e-09 ***
## vaccine_doses_administered.l6  6.431e-03  6.658e-03   0.966  0.33471    
## mobility_mean.l6               6.130e+01  4.346e+01   1.410  0.15921    
## tests_taken.l7                 8.633e-04  4.288e-03   0.201  0.84054    
## case_count.l7                 -4.138e-02  5.142e-02  -0.805  0.42145    
## vaccine_doses_administered.l7  3.935e-03  6.629e-03   0.594  0.55313    
## mobility_mean.l7               2.841e+01  4.102e+01   0.693  0.48898    
## const                         -4.659e+01  1.506e+02  -0.309  0.75718    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3039 on 379 degrees of freedom
## Multiple R-Squared: 0.5532,  Adjusted R-squared: 0.5202 
## F-statistic: 16.76 on 28 and 379 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -1.876e-02  2.918e-02  -0.643 0.520667    
## case_count.l1                 -6.359e-01  3.400e-01  -1.870 0.062196 .  
## vaccine_doses_administered.l1 -1.589e-01  4.301e-02  -3.694 0.000253 ***
## mobility_mean.l1               1.249e+02  2.661e+02   0.469 0.639007    
## tests_taken.l2                -2.066e-02  3.858e-02  -0.536 0.592562    
## case_count.l2                 -2.649e-01  3.824e-01  -0.693 0.488831    
## vaccine_doses_administered.l2 -2.347e-01  4.420e-02  -5.310 1.87e-07 ***
## mobility_mean.l2               1.186e+03  2.795e+02   4.244 2.77e-05 ***
## tests_taken.l3                -1.964e-02  4.349e-02  -0.452 0.651868    
## case_count.l3                 -5.239e-01  4.010e-01  -1.307 0.192169    
## vaccine_doses_administered.l3 -2.822e-01  4.303e-02  -6.558 1.79e-10 ***
## mobility_mean.l3               6.688e+02  2.866e+02   2.333 0.020150 *  
## tests_taken.l4                -4.556e-02  4.700e-02  -0.969 0.333007    
## case_count.l4                 -6.552e-01  4.151e-01  -1.578 0.115304    
## vaccine_doses_administered.l4 -1.900e-01  4.467e-02  -4.254 2.65e-05 ***
## mobility_mean.l4               1.103e+03  2.910e+02   3.792 0.000174 ***
## tests_taken.l5                -3.637e-02  4.400e-02  -0.827 0.409029    
## case_count.l5                 -4.807e-01  3.924e-01  -1.225 0.221393    
## vaccine_doses_administered.l5 -2.849e-01  4.355e-02  -6.542 1.97e-10 ***
## mobility_mean.l5               8.364e+02  2.917e+02   2.868 0.004365 ** 
## tests_taken.l6                -3.694e-02  3.820e-02  -0.967 0.334274    
## case_count.l6                 -7.509e-01  3.828e-01  -1.962 0.050529 .  
## vaccine_doses_administered.l6 -1.345e-01  4.412e-02  -3.049 0.002459 ** 
## mobility_mean.l6               7.774e+02  2.880e+02   2.699 0.007263 ** 
## tests_taken.l7                -3.253e-03  2.841e-02  -0.114 0.908915    
## case_count.l7                 -7.257e-02  3.407e-01  -0.213 0.831469    
## vaccine_doses_administered.l7  5.672e-01  4.393e-02  12.912  < 2e-16 ***
## mobility_mean.l7              -2.799e+01  2.718e+02  -0.103 0.918044    
## const                          1.770e+02  9.980e+02   0.177 0.859337    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 20140 on 379 degrees of freedom
## Multiple R-Squared: 0.7616,  Adjusted R-squared: 0.744 
## F-statistic: 43.25 on 28 and 379 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 2.516e-06  5.515e-06   0.456 0.648465    
## case_count.l1                 -8.401e-05  6.425e-05  -1.307 0.191843    
## vaccine_doses_administered.l1  2.158e-05  8.128e-06   2.655 0.008273 ** 
## mobility_mean.l1              -3.598e-01  5.030e-02  -7.154 4.39e-12 ***
## tests_taken.l2                 6.155e-07  7.291e-06   0.084 0.932775    
## case_count.l2                 -1.397e-04  7.226e-05  -1.933 0.053941 .  
## vaccine_doses_administered.l2 -6.160e-06  8.352e-06  -0.738 0.461274    
## mobility_mean.l2              -2.221e-01  5.281e-02  -4.205 3.26e-05 ***
## tests_taken.l3                 5.283e-06  8.219e-06   0.643 0.520747    
## case_count.l3                 -2.253e-04  7.577e-05  -2.974 0.003131 ** 
## vaccine_doses_administered.l3  6.555e-06  8.131e-06   0.806 0.420640    
## mobility_mean.l3              -1.971e-01  5.416e-02  -3.640 0.000311 ***
## tests_taken.l4                -7.577e-06  8.882e-06  -0.853 0.394132    
## case_count.l4                 -1.679e-04  7.844e-05  -2.140 0.032978 *  
## vaccine_doses_administered.l4 -1.328e-05  8.441e-06  -1.573 0.116493    
## mobility_mean.l4              -9.849e-02  5.499e-02  -1.791 0.074082 .  
## tests_taken.l5                -1.051e-05  8.315e-06  -1.264 0.207134    
## case_count.l5                 -1.356e-04  7.416e-05  -1.828 0.068347 .  
## vaccine_doses_administered.l5  5.481e-06  8.230e-06   0.666 0.505847    
## mobility_mean.l5              -1.996e-01  5.512e-02  -3.621 0.000334 ***
## tests_taken.l6                -6.699e-06  7.220e-06  -0.928 0.354089    
## case_count.l6                 -2.330e-04  7.234e-05  -3.221 0.001389 ** 
## vaccine_doses_administered.l6 -1.397e-06  8.338e-06  -0.168 0.866982    
## mobility_mean.l6              -1.061e-01  5.443e-02  -1.949 0.052024 .  
## tests_taken.l7                -6.545e-06  5.370e-06  -1.219 0.223676    
## case_count.l7                 -1.305e-04  6.439e-05  -2.026 0.043426 *  
## vaccine_doses_administered.l7 -1.974e-05  8.302e-06  -2.377 0.017936 *  
## mobility_mean.l7               1.752e-01  5.137e-02   3.411 0.000717 ***
## const                          3.654e-02  1.886e-01   0.194 0.846494    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.806 on 379 degrees of freedom
## Multiple R-Squared: 0.4037,  Adjusted R-squared: 0.3596 
## F-statistic: 9.164 on 28 and 379 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                 1252895784  1918874.9                   23332252
## case_count                     1918875  9235203.7                    4891734
## vaccine_doses_administered    23332252  4891733.7                  405589362
## mobility_mean                    -2088      881.1                      17494
##                            mobility_mean
## tests_taken                     -2088.45
## case_count                        881.07
## vaccine_doses_administered      17494.43
## mobility_mean                      14.48
## 
## Correlation matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                    1.00000    0.01784                    0.03273
## case_count                     0.01784    1.00000                    0.07993
## vaccine_doses_administered     0.03273    0.07993                    1.00000
## mobility_mean                 -0.01550    0.07618                    0.22825
##                            mobility_mean
## tests_taken                     -0.01550
## case_count                       0.07618
## vaccine_doses_administered       0.22825
## mobility_mean                    1.00000

preds=predict(fit3a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_d1)[1],1),covid_d1$case_count, type = "l")
lines(seq((dim(covid_d1)[1]-20),dim(covid_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_d1$case_count,21), type = "l",ylim=c(min(preds$fcst$case_count[,2]),max(preds$fcst$case_count[,3])))
lines(preds$fcst$case_count[,1],type = "l",col='blue')
lines(preds$fcst$case_count[,2],type = "l",col='blue', lty=2)
lines(preds$fcst$case_count[,3],type = "l",col='blue', lty=2)

short_ASE_fit3a = mean((tail(covid_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit3a

## [1] 1635425

short_ASE_fit3a^.5

## [1] 1278.838

#7 Day RMSE of 1278.8 which is second lowest short term RMSE
#Maybe try to look up rolling window version

long_ASE_fit3a = mean((tail(covid_d1$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit3a

## [1] 949245.8

long_ASE_fit3a^.5

## [1] 974.2925

#21 Day RMSE of 974.3 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest long term VAR model
#Maybe try to look up rolling window version

#Test a first differenced and seasonal data set
VARselect(covid_d1,lag.max = 25,type = 'const',season = 7)

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      7      7      7      7 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.100714e+01 6.075594e+01 6.049028e+01 6.034737e+01 5.991805e+01
## HQ(n)  6.118452e+01 6.099781e+01 6.079666e+01 6.071825e+01 6.035343e+01
## SC(n)  6.145460e+01 6.136611e+01 6.126317e+01 6.128297e+01 6.101637e+01
## FPE(n) 3.126734e+26 2.432396e+26 1.865218e+26 1.617215e+26 1.053086e+26
##                   6            7            8            9           10
## AIC(n) 5.981082e+01 5.957415e+01 5.957787e+01 5.959924e+01 5.962475e+01
## HQ(n)  6.031070e+01 6.013853e+01 6.020675e+01 6.029262e+01 6.038263e+01
## SC(n)  6.107185e+01 6.099790e+01 6.116433e+01 6.134841e+01 6.153663e+01
## FPE(n) 9.464374e+25 7.474246e+25 7.507661e+25 7.676871e+25 7.883953e+25
##                  11           12           13           14           15
## AIC(n) 5.965132e+01 5.967592e+01 5.972030e+01 5.968985e+01 5.971551e+01
## HQ(n)  6.047371e+01 6.056280e+01 6.067168e+01 6.070573e+01 6.079590e+01
## SC(n)  6.172592e+01 6.191323e+01 6.212033e+01 6.225259e+01 6.244097e+01
## FPE(n) 8.106958e+25 8.321674e+25 8.714897e+25 8.470920e+25 8.711545e+25
##                  16           17           18           19           20
## AIC(n) 5.971280e+01 5.974522e+01 5.977376e+01 5.976680e+01 5.980942e+01
## HQ(n)  6.085768e+01 6.095461e+01 6.104765e+01 6.110519e+01 6.121230e+01
## SC(n)  6.260096e+01 6.279610e+01 6.298736e+01 6.314311e+01 6.334844e+01
## FPE(n) 8.710989e+25 9.024940e+25 9.317183e+25 9.286860e+25 9.730909e+25
##                  21           22           23           24           25
## AIC(n) 5.976474e+01 5.978821e+01 5.983441e+01 5.988911e+01 5.989082e+01
## HQ(n)  6.123213e+01 6.132010e+01 6.143080e+01 6.155000e+01 6.161621e+01
## SC(n)  6.346648e+01 6.365266e+01 6.386157e+01 6.407899e+01 6.424341e+01
## FPE(n) 9.347804e+25 9.617226e+25 1.012660e+26 1.075929e+26 1.084703e+26

  #AIC 7, BIC 7

#Fit based on AIC
fit4a=VAR(covid_d1,p=7,type="const",season = 7)
summary(fit4a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean 
## Deterministic variables: const 
## Sample size: 408 
## Log Likelihood: -14314.892 
## Roots of the characteristic polynomial:
## 0.9733 0.9733 0.9478 0.9478 0.8905 0.8905  0.89  0.89 0.8379 0.8379 0.788 0.788 0.7609 0.7609 0.7495 0.7495 0.7251 0.7251 0.6716 0.6716 0.6438 0.6438 0.5927 0.5927 0.5879 0.5879 0.4473 0.4473
## Call:
## VAR(y = covid_d1, p = 7, type = "const", season = 7L)
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -9.024e-01  5.164e-02 -17.475  < 2e-16 ***
## case_count.l1                  1.343e+00  6.307e-01   2.129  0.03393 *  
## vaccine_doses_administered.l1  8.995e-02  8.404e-02   1.070  0.28517    
## mobility_mean.l1               1.645e+02  5.081e+02   0.324  0.74636    
## tests_taken.l2                -8.318e-01  6.833e-02 -12.174  < 2e-16 ***
## case_count.l2                  1.535e+00  7.249e-01   2.117  0.03491 *  
## vaccine_doses_administered.l2 -6.741e-04  8.537e-02  -0.008  0.99370    
## mobility_mean.l2               6.161e+02  5.440e+02   1.133  0.25808    
## tests_taken.l3                -8.106e-01  7.715e-02 -10.507  < 2e-16 ***
## case_count.l3                  2.008e+00  7.693e-01   2.610  0.00942 ** 
## vaccine_doses_administered.l3  7.935e-02  8.360e-02   0.949  0.34310    
## mobility_mean.l3               8.026e+02  5.564e+02   1.443  0.14999    
## tests_taken.l4                -5.907e-01  8.359e-02  -7.066 7.89e-12 ***
## case_count.l4                  5.752e-01  7.936e-01   0.725  0.46904    
## vaccine_doses_administered.l4  1.138e-01  8.717e-02   1.306  0.19242    
## mobility_mean.l4               7.874e+02  5.691e+02   1.384  0.16732    
## tests_taken.l5                -4.080e-01  7.841e-02  -5.204 3.23e-07 ***
## case_count.l5                  2.374e+00  7.512e-01   3.160  0.00170 ** 
## vaccine_doses_administered.l5  1.353e-01  8.385e-02   1.614  0.10742    
## mobility_mean.l5               6.513e+02  5.708e+02   1.141  0.25464    
## tests_taken.l6                -2.025e-01  6.837e-02  -2.962  0.00326 ** 
## case_count.l6                  1.625e+00  7.100e-01   2.289  0.02264 *  
## vaccine_doses_administered.l6 -4.232e-02  8.522e-02  -0.497  0.61979    
## mobility_mean.l6               3.422e+02  5.644e+02   0.606  0.54470    
## tests_taken.l7                -3.874e-02  5.101e-02  -0.759  0.44813    
## case_count.l7                  7.410e-01  6.088e-01   1.217  0.22435    
## vaccine_doses_administered.l7  4.837e-02  8.511e-02   0.568  0.57013    
## mobility_mean.l7               2.214e+02  5.320e+02   0.416  0.67747    
## const                          5.126e+01  1.759e+03   0.029  0.97676    
## sd1                           -7.788e+03  1.186e+04  -0.656  0.51198    
## sd2                            2.333e+03  1.324e+04   0.176  0.86024    
## sd3                            6.378e+03  1.133e+04   0.563  0.57373    
## sd4                            9.530e+03  1.130e+04   0.843  0.39956    
## sd5                           -8.522e+03  1.316e+04  -0.648  0.51766    
## sd6                            1.682e+03  1.160e+04   0.145  0.88483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35490 on 373 degrees of freedom
## Multiple R-Squared: 0.523,   Adjusted R-squared: 0.4795 
## F-statistic: 12.03 on 34 and 373 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count: 
## =========================================== 
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.494e-03  4.189e-03   0.357 0.721537    
## case_count.l1                 -6.410e-01  5.116e-02 -12.530  < 2e-16 ***
## vaccine_doses_administered.l1  1.440e-02  6.817e-03   2.113 0.035292 *  
## mobility_mean.l1               2.151e+02  4.121e+01   5.218 3.00e-07 ***
## tests_taken.l2                 1.021e-02  5.542e-03   1.842 0.066210 .  
## case_count.l2                 -6.904e-01  5.880e-02 -11.741  < 2e-16 ***
## vaccine_doses_administered.l2  7.120e-03  6.925e-03   1.028 0.304502    
## mobility_mean.l2               1.145e+02  4.412e+01   2.596 0.009808 ** 
## tests_taken.l3                 2.266e-02  6.258e-03   3.621 0.000334 ***
## case_count.l3                 -5.916e-01  6.240e-02  -9.480  < 2e-16 ***
## vaccine_doses_administered.l3  1.976e-02  6.781e-03   2.914 0.003781 ** 
## mobility_mean.l3               6.287e+01  4.513e+01   1.393 0.164427    
## tests_taken.l4                 2.337e-02  6.781e-03   3.447 0.000632 ***
## case_count.l4                 -4.674e-01  6.437e-02  -7.261 2.25e-12 ***
## vaccine_doses_administered.l4  7.785e-03  7.071e-03   1.101 0.271612    
## mobility_mean.l4              -3.720e+01  4.616e+01  -0.806 0.420771    
## tests_taken.l5                 1.990e-02  6.360e-03   3.129 0.001895 ** 
## case_count.l5                 -4.981e-01  6.094e-02  -8.174 4.72e-15 ***
## vaccine_doses_administered.l5  1.395e-02  6.801e-03   2.051 0.040943 *  
## mobility_mean.l5              -1.413e+01  4.630e+01  -0.305 0.760357    
## tests_taken.l6                 1.329e-02  5.546e-03   2.397 0.017023 *  
## case_count.l6                 -2.387e-01  5.759e-02  -4.145 4.22e-05 ***
## vaccine_doses_administered.l6  1.683e-02  6.912e-03   2.435 0.015353 *  
## mobility_mean.l6              -3.520e+01  4.578e+01  -0.769 0.442485    
## tests_taken.l7                 3.446e-03  4.138e-03   0.833 0.405427    
## case_count.l7                 -4.219e-02  4.938e-02  -0.854 0.393509    
## vaccine_doses_administered.l7  7.356e-04  6.903e-03   0.107 0.915192    
## mobility_mean.l7              -6.666e+01  4.315e+01  -1.545 0.123235    
## const                         -5.329e+01  1.427e+02  -0.374 0.708958    
## sd1                            3.982e+03  9.624e+02   4.138 4.34e-05 ***
## sd2                            2.705e+03  1.074e+03   2.519 0.012189 *  
## sd3                            8.336e+02  9.189e+02   0.907 0.364859    
## sd4                            1.390e+03  9.166e+02   1.517 0.130165    
## sd5                            1.998e+03  1.067e+03   1.872 0.062034 .  
## sd6                           -2.608e+03  9.410e+02  -2.771 0.005864 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 2879 on 373 degrees of freedom
## Multiple R-Squared: 0.6054,  Adjusted R-squared: 0.5695 
## F-statistic: 16.83 on 34 and 373 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -2.028e-02  2.855e-02  -0.710  0.47805    
## case_count.l1                 -4.863e-01  3.487e-01  -1.395  0.16397    
## vaccine_doses_administered.l1 -1.247e-01  4.647e-02  -2.684  0.00761 ** 
## mobility_mean.l1               2.147e+02  2.809e+02   0.764  0.44516    
## tests_taken.l2                -5.742e-03  3.778e-02  -0.152  0.87928    
## case_count.l2                 -3.272e-01  4.008e-01  -0.816  0.41487    
## vaccine_doses_administered.l2 -2.292e-01  4.720e-02  -4.855 1.77e-06 ***
## mobility_mean.l2               9.257e+02  3.007e+02   3.078  0.00224 ** 
## tests_taken.l3                -6.026e-03  4.265e-02  -0.141  0.88774    
## case_count.l3                 -3.578e-01  4.253e-01  -0.841  0.40076    
## vaccine_doses_administered.l3 -2.923e-01  4.622e-02  -6.323 7.33e-10 ***
## mobility_mean.l3               9.314e+02  3.076e+02   3.028  0.00263 ** 
## tests_taken.l4                -3.138e-02  4.622e-02  -0.679  0.49754    
## case_count.l4                 -2.523e-01  4.388e-01  -0.575  0.56561    
## vaccine_doses_administered.l4 -1.542e-01  4.820e-02  -3.198  0.00150 ** 
## mobility_mean.l4               9.498e+02  3.146e+02   3.019  0.00271 ** 
## tests_taken.l5                -1.505e-02  4.335e-02  -0.347  0.72873    
## case_count.l5                 -1.993e-02  4.154e-01  -0.048  0.96175    
## vaccine_doses_administered.l5 -2.795e-01  4.636e-02  -6.030 3.96e-09 ***
## mobility_mean.l5               6.219e+02  3.156e+02   1.971  0.04951 *  
## tests_taken.l6                -2.482e-02  3.780e-02  -0.657  0.51185    
## case_count.l6                 -6.294e-01  3.926e-01  -1.603  0.10968    
## vaccine_doses_administered.l6 -8.583e-02  4.712e-02  -1.822  0.06929 .  
## mobility_mean.l6               3.081e+02  3.120e+02   0.987  0.32408    
## tests_taken.l7                 4.936e-03  2.820e-02   0.175  0.86117    
## case_count.l7                 -1.116e-01  3.366e-01  -0.332  0.74033    
## vaccine_doses_administered.l7  4.797e-01  4.705e-02  10.195  < 2e-16 ***
## mobility_mean.l7               8.756e+01  2.941e+02   0.298  0.76610    
## const                          1.835e+02  9.724e+02   0.189  0.85046    
## sd1                           -1.783e+04  6.560e+03  -2.717  0.00689 ** 
## sd2                           -1.041e+04  7.321e+03  -1.422  0.15577    
## sd3                           -9.238e+03  6.263e+03  -1.475  0.14106    
## sd4                           -1.032e+04  6.248e+03  -1.651  0.09956 .  
## sd5                           -2.163e+04  7.276e+03  -2.973  0.00314 ** 
## sd6                           -2.768e+04  6.414e+03  -4.316 2.04e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 19620 on 373 degrees of freedom
## Multiple R-Squared: 0.7773,  Adjusted R-squared: 0.757 
## F-statistic: 38.29 on 34 and 373 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.296e-06  5.363e-06   0.242  0.80918    
## case_count.l1                 -1.269e-04  6.549e-05  -1.938  0.05339 .  
## vaccine_doses_administered.l1  8.216e-06  8.728e-06   0.941  0.34710    
## mobility_mean.l1              -3.012e-01  5.277e-02  -5.708 2.33e-08 ***
## tests_taken.l2                -1.486e-06  7.096e-06  -0.209  0.83428    
## case_count.l2                 -1.473e-04  7.528e-05  -1.956  0.05117 .  
## vaccine_doses_administered.l2 -4.498e-06  8.865e-06  -0.507  0.61223    
## mobility_mean.l2              -1.829e-01  5.649e-02  -3.239  0.00131 ** 
## tests_taken.l3                 3.995e-06  8.012e-06   0.499  0.61832    
## case_count.l3                 -2.374e-04  7.989e-05  -2.972  0.00315 ** 
## vaccine_doses_administered.l3  3.982e-06  8.681e-06   0.459  0.64672    
## mobility_mean.l3              -1.846e-01  5.778e-02  -3.194  0.00152 ** 
## tests_taken.l4                -7.695e-06  8.681e-06  -0.886  0.37594    
## case_count.l4                 -2.020e-04  8.241e-05  -2.451  0.01470 *  
## vaccine_doses_administered.l4 -5.125e-06  9.053e-06  -0.566  0.57164    
## mobility_mean.l4              -1.058e-01  5.910e-02  -1.791  0.07416 .  
## tests_taken.l5                -1.032e-05  8.143e-06  -1.267  0.20594    
## case_count.l5                 -1.527e-04  7.802e-05  -1.957  0.05106 .  
## vaccine_doses_administered.l5 -4.120e-06  8.708e-06  -0.473  0.63637    
## mobility_mean.l5              -1.496e-01  5.928e-02  -2.524  0.01202 *  
## tests_taken.l6                -7.414e-06  7.100e-06  -1.044  0.29709    
## case_count.l6                 -1.595e-04  7.373e-05  -2.164  0.03112 *  
## vaccine_doses_administered.l6  3.323e-06  8.850e-06   0.376  0.70750    
## mobility_mean.l6              -6.305e-02  5.861e-02  -1.076  0.28276    
## tests_taken.l7                -5.002e-06  5.298e-06  -0.944  0.34564    
## case_count.l7                 -1.170e-04  6.323e-05  -1.851  0.06497 .  
## vaccine_doses_administered.l7 -6.161e-06  8.838e-06  -0.697  0.48617    
## mobility_mean.l7               5.284e-02  5.524e-02   0.956  0.33945    
## const                          3.120e-02  1.826e-01   0.171  0.86445    
## sd1                            3.584e+00  1.232e+00   2.909  0.00384 ** 
## sd2                            3.597e+00  1.375e+00   2.616  0.00925 ** 
## sd3                            3.023e+00  1.176e+00   2.569  0.01058 *  
## sd4                            9.644e-01  1.173e+00   0.822  0.41173    
## sd5                            6.401e+00  1.367e+00   4.683 3.96e-06 ***
## sd6                            1.929e+00  1.205e+00   1.601  0.11027    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.686 on 373 degrees of freedom
## Multiple R-Squared: 0.4496,  Adjusted R-squared: 0.3994 
## F-statistic: 8.962 on 34 and 373 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                  1.260e+09  3044527.2                   18250514
## case_count                   3.045e+06  8287127.6                    3153308
## vaccine_doses_administered   1.825e+07  3153308.2                  385036896
## mobility_mean                2.713e+02      415.7                      19863
##                            mobility_mean
## tests_taken                       271.26
## case_count                        415.72
## vaccine_doses_administered      19862.67
## mobility_mean                      13.58
## 
## Correlation matrix of residuals:
##                            tests_taken case_count vaccine_doses_administered
## tests_taken                   1.000000    0.02980                    0.02621
## case_count                    0.029799    1.00000                    0.05582
## vaccine_doses_administered    0.026207    0.05582                    1.00000
## mobility_mean                 0.002074    0.03918                    0.27465
##                            mobility_mean
## tests_taken                     0.002074
## case_count                      0.039182
## vaccine_doses_administered      0.274647
## mobility_mean                   1.000000

preds=predict(fit4a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_d1)[1],1),covid_d1$case_count, type = "l")
lines(seq((dim(covid_d1)[1]-20),dim(covid_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_d1$case_count,21), type = "l",ylim=c(-3900,4600))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit4a = mean((tail(covid_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit4a

## [1] 1306929

short_ASE_fit4a^.5

## [1] 1143.21

#7 Day RMSE of 1143.2 which is lowest short term RMSE
#Maybe try to look up rolling window version

long_ASE_fit4a = mean((tail(covid_d1$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit4a

## [1] 1405555

long_ASE_fit4a^.5

## [1] 1185.561

#21 Day RMSE of 1185.6 which is much lower than the 3806 from our ARIMA(6,1,14) model and second lowest model
#Maybe try to look up rolling window version

#Create first different response only data set
names(covid_reduced)

## [1] "tests_taken"                "case_count"                
## [3] "vaccine_doses_administered" "mobility_mean"

cases_d1=artrans.wge(covid_reduced$case_count,1)

covid_reduced_cases_d1=covid_reduced
covid_reduced_cases_d1$case_count_d1=c(NA,cases_d1)
names(covid_reduced_cases_d1)

## [1] "tests_taken"                "case_count"                
## [3] "vaccine_doses_administered" "mobility_mean"             
## [5] "case_count_d1"

covid_reduced_cases_d1=covid_reduced_cases_d1[2:dim(covid_reduced_cases_d1)[1],c(1,3,4,5)]
str(covid_reduced_cases_d1)

## 'data.frame':    415 obs. of  4 variables:
##  $ tests_taken               : int  57352 51106 104858 124061 33404 31019 54382 79339 123081 55937 ...
##  $ vaccine_doses_administered: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ mobility_mean             : num  -11.33 -11 -10.17 -11 -5.17 ...
##  $ case_count_d1             : num  1372 684 -1979 -625 405 ...

#Test a first differenced cases only without seasonality
VARselect(covid_reduced_cases_d1,lag.max = 25,type = 'const')

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      8      8      8      8 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.213069e+01 6.174882e+01 6.153838e+01 6.133380e+01 6.096615e+01
## HQ(n)  6.221132e+01 6.189394e+01 6.174801e+01 6.160793e+01 6.130478e+01
## SC(n)  6.233408e+01 6.211492e+01 6.206720e+01 6.202534e+01 6.182040e+01
## FPE(n) 9.616524e+26 6.564251e+26 5.318900e+26 4.335397e+26 3.002242e+26
##                   6            7            8            9           10
## AIC(n) 6.037371e+01 6.012685e+01 5.974183e+01 5.976261e+01 5.974824e+01
## HQ(n)  6.077684e+01 6.059448e+01 6.027396e+01 6.035924e+01 6.040937e+01
## SC(n)  6.139067e+01 6.130653e+01 6.108422e+01 6.126771e+01 6.141606e+01
## FPE(n) 1.660634e+26 1.297893e+26 8.835923e+25 9.027433e+25 8.906074e+25
##                  11           12           13           14           15
## AIC(n) 5.975888e+01 5.978012e+01 5.980467e+01 5.980010e+01 5.977352e+01
## HQ(n)  6.048452e+01 6.057025e+01 6.065930e+01 6.071924e+01 6.075716e+01
## SC(n)  6.158941e+01 6.177337e+01 6.196063e+01 6.211877e+01 6.225490e+01
## FPE(n) 9.010459e+25 9.215016e+25 9.457529e+25 9.430139e+25 9.200426e+25
##                  16           17           18           19           20
## AIC(n) 5.980352e+01 5.980417e+01 5.982964e+01 5.986458e+01 5.988051e+01
## HQ(n)  6.085165e+01 6.091680e+01 6.100678e+01 6.110622e+01 6.118665e+01
## SC(n)  6.244761e+01 6.261098e+01 6.279917e+01 6.299682e+01 6.317546e+01
## FPE(n) 9.501444e+25 9.531393e+25 9.804882e+25 1.018559e+26 1.038550e+26
##                  21           22           23           24           25
## AIC(n) 5.990528e+01 5.984448e+01 5.985995e+01 5.990928e+01 5.995581e+01
## HQ(n)  6.127592e+01 6.127962e+01 6.135959e+01 6.147342e+01 6.158445e+01
## SC(n)  6.336295e+01 6.346486e+01 6.364305e+01 6.385509e+01 6.406433e+01
## FPE(n) 1.068755e+26 1.010037e+26 1.030647e+26 1.088383e+26 1.146677e+26

  #AIC 8, BIC 8

#Fit based on AIC
fit5a=VAR(covid_reduced_cases_d1,p=8,type="const")
summary(fit5a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1 
## Deterministic variables: const 
## Sample size: 407 
## Log Likelihood: -14316.568 
## Roots of the characteristic polynomial:
## 0.9871 0.9871 0.9842 0.9842 0.9839 0.9839 0.9477 0.9477 0.9347 0.9347 0.9292 0.9055 0.9055 0.8145 0.8145 0.7989 0.7989 0.7967 0.7967 0.7533 0.7533 0.7074 0.7074 0.6792 0.6792 0.657 0.657 0.6369 0.6369 0.6036 0.2768 0.1779
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const")
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 8.206e-02  5.170e-02   1.587 0.113262    
## vaccine_doses_administered.l1  6.594e-02  7.651e-02   0.862 0.389345    
## mobility_mean.l1               3.913e+02  4.802e+02   0.815 0.415632    
## case_count_d1.l1               1.367e+00  6.065e-01   2.254 0.024805 *  
## tests_taken.l2                 5.245e-02  5.125e-02   1.024 0.306729    
## vaccine_doses_administered.l2 -1.765e-02  8.693e-02  -0.203 0.839169    
## mobility_mean.l2               1.488e+02  5.385e+02   0.276 0.782532    
## case_count_d1.l2               1.867e+00  7.083e-01   2.635 0.008753 ** 
## tests_taken.l3                 4.560e-03  5.026e-02   0.091 0.927751    
## vaccine_doses_administered.l3  4.477e-02  8.699e-02   0.515 0.607075    
## mobility_mean.l3              -2.184e+01  5.467e+02  -0.040 0.968164    
## case_count_d1.l3               2.366e+00  8.096e-01   2.922 0.003687 ** 
## tests_taken.l4                 2.039e-01  4.973e-02   4.099 5.08e-05 ***
## vaccine_doses_administered.l4  3.848e-02  8.641e-02   0.445 0.656304    
## mobility_mean.l4               3.315e+01  5.394e+02   0.061 0.951028    
## case_count_d1.l4               6.854e-01  8.224e-01   0.833 0.405098    
## tests_taken.l5                 1.610e-01  4.947e-02   3.255 0.001237 ** 
## vaccine_doses_administered.l5 -3.761e-02  8.656e-02  -0.434 0.664229    
## mobility_mean.l5               1.507e+02  5.379e+02   0.280 0.779550    
## case_count_d1.l5               2.369e+00  8.059e-01   2.939 0.003494 ** 
## tests_taken.l6                 1.912e-01  4.984e-02   3.837 0.000146 ***
## vaccine_doses_administered.l6 -1.348e-01  8.719e-02  -1.546 0.122946    
## mobility_mean.l6              -2.336e+02  5.376e+02  -0.434 0.664198    
## case_count_d1.l6               1.762e+00  8.045e-01   2.190 0.029115 *  
## tests_taken.l7                 1.655e-01  5.098e-02   3.246 0.001276 ** 
## vaccine_doses_administered.l7  1.102e-01  8.773e-02   1.256 0.210034    
## mobility_mean.l7              -4.344e+02  5.351e+02  -0.812 0.417417    
## case_count_d1.l7               7.334e-01  7.069e-01   1.037 0.300189    
## tests_taken.l8                 3.408e-02  5.142e-02   0.663 0.507804    
## vaccine_doses_administered.l8 -8.336e-02  7.776e-02  -1.072 0.284424    
## mobility_mean.l8               2.913e+01  4.836e+02   0.060 0.951988    
## case_count_d1.l8               3.535e-01  6.008e-01   0.588 0.556644    
## const                          1.197e+04  6.406e+03   1.869 0.062474 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35410 on 374 degrees of freedom
## Multiple R-Squared: 0.4636,  Adjusted R-squared: 0.4177 
## F-statistic:  10.1 on 32 and 374 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -1.966e-02  2.924e-02  -0.672 0.501780    
## vaccine_doses_administered.l1  8.261e-01  4.328e-02  19.089  < 2e-16 ***
## mobility_mean.l1               8.960e+01  2.716e+02   0.330 0.741673    
## case_count_d1.l1              -6.734e-01  3.431e-01  -1.963 0.050397 .  
## tests_taken.l2                -3.436e-03  2.899e-02  -0.119 0.905716    
## vaccine_doses_administered.l2 -7.319e-02  4.917e-02  -1.489 0.137437    
## mobility_mean.l2               1.028e+03  3.046e+02   3.375 0.000816 ***
## case_count_d1.l2              -2.631e-01  4.006e-01  -0.657 0.511685    
## tests_taken.l3                 1.963e-04  2.843e-02   0.007 0.994493    
## vaccine_doses_administered.l3 -5.240e-02  4.920e-02  -1.065 0.287579    
## mobility_mean.l3              -5.690e+02  3.092e+02  -1.840 0.066560 .  
## case_count_d1.l3              -4.891e-01  4.579e-01  -1.068 0.286200    
## tests_taken.l4                -2.612e-02  2.813e-02  -0.929 0.353576    
## vaccine_doses_administered.l4  8.887e-02  4.887e-02   1.818 0.069812 .  
## mobility_mean.l4               4.106e+02  3.051e+02   1.346 0.179122    
## case_count_d1.l4              -6.412e-01  4.651e-01  -1.378 0.168875    
## tests_taken.l5                 4.957e-03  2.798e-02   0.177 0.859493    
## vaccine_doses_administered.l5 -1.002e-01  4.896e-02  -2.046 0.041491 *  
## mobility_mean.l5              -2.760e+02  3.042e+02  -0.907 0.364871    
## case_count_d1.l5              -4.551e-01  4.558e-01  -0.998 0.318721    
## tests_taken.l6                -3.422e-03  2.819e-02  -0.121 0.903444    
## vaccine_doses_administered.l6  1.475e-01  4.932e-02   2.991 0.002966 ** 
## mobility_mean.l6              -9.781e+01  3.041e+02  -0.322 0.747893    
## case_count_d1.l6              -7.274e-01  4.551e-01  -1.598 0.110803    
## tests_taken.l7                 3.102e-02  2.883e-02   1.076 0.282670    
## vaccine_doses_administered.l7  6.992e-01  4.962e-02  14.091  < 2e-16 ***
## mobility_mean.l7              -8.339e+02  3.026e+02  -2.755 0.006152 ** 
## case_count_d1.l7              -3.997e-02  3.998e-01  -0.100 0.920423    
## tests_taken.l8                 7.617e-04  2.908e-02   0.026 0.979117    
## vaccine_doses_administered.l8 -5.634e-01  4.398e-02 -12.810  < 2e-16 ***
## mobility_mean.l8              -7.604e+01  2.735e+02  -0.278 0.781143    
## case_count_d1.l8               1.090e-01  3.398e-01   0.321 0.748617    
## const                          6.916e+02  3.623e+03   0.191 0.848720    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 20030 on 374 degrees of freedom
## Multiple R-Squared: 0.9406,  Adjusted R-squared: 0.9355 
## F-statistic: 185.1 on 32 and 374 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.512e-06  5.485e-06   0.276 0.782941    
## vaccine_doses_administered.l1  1.885e-05  8.118e-06   2.322 0.020767 *  
## mobility_mean.l1               6.149e-01  5.095e-02  12.068  < 2e-16 ***
## case_count_d1.l1              -7.481e-05  6.435e-05  -1.162 0.245777    
## tests_taken.l2                -3.554e-06  5.438e-06  -0.654 0.513759    
## vaccine_doses_administered.l2 -2.611e-05  9.223e-06  -2.831 0.004885 ** 
## mobility_mean.l2               1.248e-01  5.714e-02   2.185 0.029531 *  
## case_count_d1.l2              -1.094e-04  7.515e-05  -1.456 0.146267    
## tests_taken.l3                 2.837e-06  5.332e-06   0.532 0.595062    
## vaccine_doses_administered.l3  1.325e-05  9.230e-06   1.435 0.151987    
## mobility_mean.l3               6.513e-03  5.801e-02   0.112 0.910664    
## case_count_d1.l3              -1.686e-04  8.590e-05  -1.963 0.050392 .  
## tests_taken.l4                -1.322e-05  5.276e-06  -2.506 0.012618 *  
## vaccine_doses_administered.l4 -2.023e-05  9.168e-06  -2.206 0.027982 *  
## mobility_mean.l4               8.589e-02  5.723e-02   1.501 0.134269    
## case_count_d1.l4              -1.183e-04  8.725e-05  -1.356 0.175879    
## tests_taken.l5                -5.799e-06  5.249e-06  -1.105 0.269951    
## vaccine_doses_administered.l5  1.870e-05  9.185e-06   2.036 0.042501 *  
## mobility_mean.l5              -1.010e-01  5.707e-02  -1.770 0.077613 .  
## case_count_d1.l5              -8.204e-05  8.551e-05  -0.959 0.337947    
## tests_taken.l6                 1.441e-06  5.288e-06   0.273 0.785333    
## vaccine_doses_administered.l6 -6.599e-06  9.251e-06  -0.713 0.476127    
## mobility_mean.l6               7.569e-02  5.704e-02   1.327 0.185351    
## case_count_d1.l6              -1.744e-04  8.536e-05  -2.043 0.041746 *  
## tests_taken.l7                -1.299e-06  5.409e-06  -0.240 0.810287    
## vaccine_doses_administered.l7 -1.784e-05  9.309e-06  -1.917 0.055999 .  
## mobility_mean.l7               2.708e-01  5.677e-02   4.770 2.64e-06 ***
## case_count_d1.l7              -8.357e-05  7.501e-05  -1.114 0.265916    
## tests_taken.l8                 4.925e-06  5.455e-06   0.903 0.367234    
## vaccine_doses_administered.l8  2.115e-05  8.251e-06   2.564 0.010742 *  
## mobility_mean.l8              -1.952e-01  5.131e-02  -3.804 0.000166 ***
## case_count_d1.l8               7.627e-05  6.374e-05   1.196 0.232266    
## const                          4.366e-02  6.797e-01   0.064 0.948815    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.757 on 374 degrees of freedom
## Multiple R-Squared: 0.7429,  Adjusted R-squared: 0.7209 
## F-statistic: 33.77 on 32 and 374 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count_d1: 
## ============================================== 
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.163e-03  4.335e-03   0.268 0.788599    
## vaccine_doses_administered.l1  2.957e-02  6.416e-03   4.608 5.58e-06 ***
## mobility_mean.l1               1.431e+02  4.027e+01   3.553 0.000430 ***
## case_count_d1.l1              -6.563e-01  5.086e-02 -12.904  < 2e-16 ***
## tests_taken.l2                 6.897e-03  4.297e-03   1.605 0.109344    
## vaccine_doses_administered.l2 -2.569e-02  7.289e-03  -3.525 0.000476 ***
## mobility_mean.l2              -4.031e+01  4.516e+01  -0.893 0.372659    
## case_count_d1.l2              -7.422e-01  5.939e-02 -12.497  < 2e-16 ***
## tests_taken.l3                 9.440e-03  4.214e-03   2.240 0.025672 *  
## vaccine_doses_administered.l3  8.050e-03  7.294e-03   1.104 0.270471    
## mobility_mean.l3              -2.382e+01  4.585e+01  -0.519 0.603735    
## case_count_d1.l3              -6.583e-01  6.789e-02  -9.696  < 2e-16 ***
## tests_taken.l4                -1.941e-03  4.170e-03  -0.465 0.641908    
## vaccine_doses_administered.l4 -8.851e-03  7.246e-03  -1.221 0.222668    
## mobility_mean.l4              -9.732e+01  4.523e+01  -2.152 0.032061 *  
## case_count_d1.l4              -5.614e-01  6.896e-02  -8.141 5.88e-15 ***
## tests_taken.l5                -4.108e-03  4.148e-03  -0.990 0.322663    
## vaccine_doses_administered.l5  1.006e-02  7.259e-03   1.385 0.166751    
## mobility_mean.l5               2.251e+01  4.510e+01   0.499 0.618078    
## case_count_d1.l5              -6.381e-01  6.757e-02  -9.443  < 2e-16 ***
## tests_taken.l6                -7.054e-03  4.179e-03  -1.688 0.092242 .  
## vaccine_doses_administered.l6 -8.497e-03  7.311e-03  -1.162 0.245910    
## mobility_mean.l6               7.078e+01  4.508e+01   1.570 0.117266    
## case_count_d1.l6              -3.599e-01  6.746e-02  -5.335 1.66e-07 ***
## tests_taken.l7                -1.052e-02  4.275e-03  -2.461 0.014298 *  
## vaccine_doses_administered.l7 -2.944e-03  7.357e-03  -0.400 0.689220    
## mobility_mean.l7              -2.825e+01  4.487e+01  -0.630 0.529345    
## case_count_d1.l7              -3.814e-02  5.928e-02  -0.643 0.520313    
## tests_taken.l8                -6.414e-04  4.311e-03  -0.149 0.881805    
## vaccine_doses_administered.l8 -5.119e-03  6.520e-03  -0.785 0.432927    
## mobility_mean.l8              -2.654e+01  4.055e+01  -0.654 0.513213    
## case_count_d1.l8               2.403e-02  5.038e-02   0.477 0.633656    
## const                          1.057e+03  5.372e+02   1.967 0.049884 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 2969 on 374 degrees of freedom
## Multiple R-Squared: 0.5756,  Adjusted R-squared: 0.5393 
## F-statistic: 15.85 on 32 and 374 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                 1253878482                   22092309      -3099.80
## vaccine_doses_administered    22092309                  401126578      16301.17
## mobility_mean                    -3100                      16301         14.12
## case_count_d1                   626054                    4299342        942.69
##                            case_count_d1
## tests_taken                     626054.2
## vaccine_doses_administered     4299342.4
## mobility_mean                      942.7
## case_count_d1                  8816244.0
## 
## Correlation matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                   1.000000                    0.03115       -0.0233
## vaccine_doses_administered    0.031151                    1.00000        0.2166
## mobility_mean                -0.023300                    0.21663        1.0000
## case_count_d1                 0.005954                    0.07230        0.0845
##                            case_count_d1
## tests_taken                     0.005954
## vaccine_doses_administered      0.072297
## mobility_mean                   0.084504
## case_count_d1                   1.000000

preds=predict(fit5a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(-3900,4600))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit5a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit5a

## [1] 1690468

short_ASE_fit5a^.5

## [1] 1300.18

#7 Day RMSE of 1300.18
#Maybe try to look up rolling window version

long_ASE_fit5a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit5a

## [1] 988749

long_ASE_fit5a^.5

## [1] 994.3586

#21 Day RMSE of 994.35 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE

#Test a first differenced cases only with seasonality
VARselect(covid_reduced_cases_d1,lag.max = 25,type = 'const',season = 7)

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      8      8      6      8 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) 6.096730e+01 6.069809e+01 6.057679e+01 6.040478e+01 6.015873e+01
## HQ(n)  6.114468e+01 6.093997e+01 6.088317e+01 6.077566e+01 6.059411e+01
## SC(n)  6.141477e+01 6.130827e+01 6.134968e+01 6.134039e+01 6.125705e+01
## FPE(n) 3.004622e+26 2.295688e+26 2.033759e+26 1.712783e+26 1.339642e+26
##                   6            7            8            9           10
## AIC(n) 5.984485e+01 5.979697e+01 5.956566e+01 5.958146e+01 5.960094e+01
## HQ(n)  6.034473e+01 6.036135e+01 6.019454e+01 6.027484e+01 6.035882e+01
## SC(n)  6.110588e+01 6.122071e+01 6.115211e+01 6.133063e+01 6.151283e+01
## FPE(n) 9.791971e+25 9.339747e+25 7.416529e+25 7.541602e+25 7.698485e+25
##                  11           12           13           14           15
## AIC(n) 5.962148e+01 5.963612e+01 5.966610e+01 5.968912e+01 5.967635e+01
## HQ(n)  6.044386e+01 6.052301e+01 6.061749e+01 6.070501e+01 6.075673e+01
## SC(n)  6.169608e+01 6.187344e+01 6.206613e+01 6.225187e+01 6.240180e+01
## FPE(n) 7.868559e+25 7.996984e+25 8.255149e+25 8.464811e+25 8.376946e+25
##                  16           17           18           19           20
## AIC(n) 5.970664e+01 5.970932e+01 5.973355e+01 5.975903e+01 5.976621e+01
## HQ(n)  6.085153e+01 6.091871e+01 6.100744e+01 6.109742e+01 6.116910e+01
## SC(n)  6.259481e+01 6.276020e+01 6.294715e+01 6.313534e+01 6.330523e+01
## FPE(n) 8.657573e+25 8.706670e+25 8.949973e+25 9.214948e+25 9.319421e+25
##                  21           22           23           24           25
## AIC(n) 5.980015e+01 5.975771e+01 5.978555e+01 5.983022e+01 5.986975e+01
## HQ(n)  6.126754e+01 6.128960e+01 6.138194e+01 6.149111e+01 6.159514e+01
## SC(n)  6.350189e+01 6.362216e+01 6.381272e+01 6.402010e+01 6.422234e+01
## FPE(n) 9.684737e+25 9.328368e+25 9.643789e+25 1.014399e+26 1.062089e+26

  #AIC 8, BIC 8

#Fit based on AIC
fit6a=VAR(covid_reduced_cases_d1,p=8,type="const",season = 7)
summary(fit6a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1 
## Deterministic variables: const 
## Sample size: 407 
## Log Likelihood: -14255.72 
## Roots of the characteristic polynomial:
## 0.9841 0.9841 0.9737 0.9737 0.948 0.948 0.9274 0.9033 0.9033 0.8907 0.8907 0.849 0.849 0.795 0.795 0.7874 0.7874 0.767 0.767 0.7257 0.7257 0.7025 0.7025 0.6991 0.6767 0.6767 0.6408 0.6408 0.5814 0.5814 0.3624 0.2511
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const", season = 7L)
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 8.333e-02  5.208e-02   1.600 0.110470    
## vaccine_doses_administered.l1  9.619e-02  8.482e-02   1.134 0.257499    
## mobility_mean.l1               1.313e+02  5.195e+02   0.253 0.800632    
## case_count_d1.l1               1.216e+00  6.421e-01   1.894 0.058977 .  
## tests_taken.l2                 5.396e-02  5.172e-02   1.043 0.297555    
## vaccine_doses_administered.l2 -8.942e-02  1.057e-01  -0.846 0.397978    
## mobility_mean.l2               4.686e+02  6.298e+02   0.744 0.457374    
## case_count_d1.l2               1.477e+00  7.562e-01   1.953 0.051593 .  
## tests_taken.l3                 4.349e-03  5.083e-02   0.086 0.931857    
## vaccine_doses_administered.l3  7.423e-02  1.045e-01   0.711 0.477782    
## mobility_mean.l3               1.640e+02  6.345e+02   0.259 0.796142    
## case_count_d1.l3               2.053e+00  8.540e-01   2.404 0.016697 *  
## tests_taken.l4                 2.094e-01  5.046e-02   4.150 4.14e-05 ***
## vaccine_doses_administered.l4  3.472e-02  1.041e-01   0.334 0.738887    
## mobility_mean.l4              -1.469e+01  6.328e+02  -0.023 0.981492    
## case_count_d1.l4               6.219e-01  8.717e-01   0.713 0.476021    
## tests_taken.l5                 1.639e-01  5.025e-02   3.262 0.001210 ** 
## vaccine_doses_administered.l5  1.988e-02  1.043e-01   0.191 0.848917    
## mobility_mean.l5              -1.095e+02  6.305e+02  -0.174 0.862259    
## case_count_d1.l5               2.469e+00  8.539e-01   2.892 0.004059 ** 
## tests_taken.l6                 1.912e-01  5.083e-02   3.762 0.000196 ***
## vaccine_doses_administered.l6 -1.781e-01  1.048e-01  -1.699 0.090247 .  
## mobility_mean.l6              -3.290e+02  6.297e+02  -0.522 0.601652    
## case_count_d1.l6               1.760e+00  8.354e-01   2.107 0.035822 *  
## tests_taken.l7                 1.543e-01  5.197e-02   2.969 0.003187 ** 
## vaccine_doses_administered.l7  8.960e-02  1.063e-01   0.843 0.399956    
## mobility_mean.l7              -9.509e+01  6.265e+02  -0.152 0.879442    
## case_count_d1.l7               8.859e-01  7.186e-01   1.233 0.218442    
## tests_taken.l8                 3.202e-02  5.237e-02   0.611 0.541396    
## vaccine_doses_administered.l8 -6.130e-02  8.569e-02  -0.715 0.474788    
## mobility_mean.l8              -1.771e+02  5.386e+02  -0.329 0.742485    
## case_count_d1.l8               3.954e-01  6.114e-01   0.647 0.518249    
## const                          1.195e+04  6.424e+03   1.860 0.063734 .  
## sd1                           -8.726e+03  1.194e+04  -0.731 0.465412    
## sd2                            1.527e+03  1.334e+04   0.114 0.908911    
## sd3                            6.752e+03  1.136e+04   0.595 0.552464    
## sd4                            1.006e+04  1.131e+04   0.889 0.374573    
## sd5                           -8.065e+03  1.318e+04  -0.612 0.540949    
## sd6                            1.595e+03  1.165e+04   0.137 0.891177    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35500 on 368 degrees of freedom
## Multiple R-Squared: 0.4696,  Adjusted R-squared: 0.4149 
## F-statistic: 8.575 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -2.152e-02  2.864e-02  -0.751  0.45291    
## vaccine_doses_administered.l1  8.631e-01  4.665e-02  18.503  < 2e-16 ***
## mobility_mean.l1               1.663e+02  2.857e+02   0.582  0.56088    
## case_count_d1.l1              -5.244e-01  3.531e-01  -1.485  0.13840    
## tests_taken.l2                 1.237e-02  2.845e-02   0.435  0.66399    
## vaccine_doses_administered.l2 -1.067e-01  5.811e-02  -1.836  0.06719 .  
## mobility_mean.l2               6.954e+02  3.464e+02   2.007  0.04543 *  
## case_count_d1.l2              -3.295e-01  4.159e-01  -0.792  0.42869    
## tests_taken.l3                -1.810e-03  2.796e-02  -0.065  0.94841    
## vaccine_doses_administered.l3 -6.832e-02  5.745e-02  -1.189  0.23510    
## mobility_mean.l3              -3.349e+01  3.489e+02  -0.096  0.92360    
## case_count_d1.l3              -3.185e-01  4.696e-01  -0.678  0.49810    
## tests_taken.l4                -2.497e-02  2.775e-02  -0.900  0.36874    
## vaccine_doses_administered.l4  1.368e-01  5.723e-02   2.389  0.01738 *  
## mobility_mean.l4              -3.683e+00  3.480e+02  -0.011  0.99156    
## case_count_d1.l4              -2.335e-01  4.794e-01  -0.487  0.62652    
## tests_taken.l5                 1.212e-02  2.763e-02   0.439  0.66117    
## vaccine_doses_administered.l5 -1.284e-01  5.735e-02  -2.239  0.02573 *  
## mobility_mean.l5              -3.370e+02  3.467e+02  -0.972  0.33166    
## case_count_d1.l5               2.113e-02  4.696e-01   0.045  0.96414    
## tests_taken.l6                -1.230e-02  2.796e-02  -0.440  0.66015    
## vaccine_doses_administered.l6  1.904e-01  5.766e-02   3.302  0.00105 ** 
## mobility_mean.l6              -3.515e+02  3.463e+02  -1.015  0.31081    
## case_count_d1.l6              -5.690e-01  4.595e-01  -1.239  0.21632    
## tests_taken.l7                 2.763e-02  2.858e-02   0.967  0.33429    
## vaccine_doses_administered.l7  5.656e-01  5.847e-02   9.672  < 2e-16 ***
## mobility_mean.l7              -2.586e+02  3.445e+02  -0.751  0.45333    
## case_count_d1.l7              -2.550e-02  3.952e-01  -0.065  0.94859    
## tests_taken.l8                -6.493e-03  2.880e-02  -0.225  0.82178    
## vaccine_doses_administered.l8 -4.770e-01  4.713e-02 -10.121  < 2e-16 ***
## mobility_mean.l8              -1.991e+02  2.962e+02  -0.672  0.50181    
## case_count_d1.l8               1.754e-01  3.363e-01   0.522  0.60227    
## const                          4.138e+02  3.533e+03   0.117  0.90683    
## sd1                           -1.872e+04  6.567e+03  -2.851  0.00460 ** 
## sd2                           -1.070e+04  7.337e+03  -1.458  0.14570    
## sd3                           -8.764e+03  6.245e+03  -1.403  0.16134    
## sd4                           -9.777e+03  6.220e+03  -1.572  0.11685    
## sd5                           -2.127e+04  7.248e+03  -2.934  0.00356 ** 
## sd6                           -2.693e+04  6.408e+03  -4.203 3.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 19520 on 368 degrees of freedom
## Multiple R-Squared: 0.9445,  Adjusted R-squared: 0.9387 
## F-statistic: 164.7 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.571e-07  5.339e-06   0.029  0.97653    
## vaccine_doses_administered.l1  6.011e-06  8.695e-06   0.691  0.48976    
## mobility_mean.l1               6.730e-01  5.325e-02  12.638  < 2e-16 ***
## case_count_d1.l1              -1.158e-04  6.582e-05  -1.760  0.07922 .  
## tests_taken.l2                -4.497e-06  5.302e-06  -0.848  0.39692    
## vaccine_doses_administered.l2 -1.146e-05  1.083e-05  -1.058  0.29067    
## mobility_mean.l2               1.036e-01  6.456e-02   1.604  0.10960    
## case_count_d1.l2              -1.201e-04  7.752e-05  -1.550  0.12203    
## tests_taken.l3                 3.565e-06  5.211e-06   0.684  0.49428    
## vaccine_doses_administered.l3  7.944e-06  1.071e-05   0.742  0.45864    
## mobility_mean.l3              -1.292e-02  6.504e-02  -0.199  0.84261    
## case_count_d1.l3              -1.874e-04  8.754e-05  -2.141  0.03293 *  
## tests_taken.l4                -1.210e-05  5.173e-06  -2.339  0.01989 *  
## vaccine_doses_administered.l4 -9.375e-06  1.067e-05  -0.879  0.38011    
## mobility_mean.l4               7.083e-02  6.487e-02   1.092  0.27555    
## case_count_d1.l4              -1.581e-04  8.936e-05  -1.770  0.07759 .  
## tests_taken.l5                -5.268e-06  5.151e-06  -1.023  0.30710    
## vaccine_doses_administered.l5  1.754e-06  1.069e-05   0.164  0.86974    
## mobility_mean.l5              -4.643e-02  6.463e-02  -0.718  0.47292    
## case_count_d1.l5              -1.032e-04  8.753e-05  -1.179  0.23915    
## tests_taken.l6                 7.607e-07  5.211e-06   0.146  0.88402    
## vaccine_doses_administered.l6  7.434e-06  1.075e-05   0.692  0.48960    
## mobility_mean.l6               6.931e-02  6.455e-02   1.074  0.28368    
## case_count_d1.l6              -1.032e-04  8.564e-05  -1.205  0.22885    
## tests_taken.l7                 1.017e-06  5.327e-06   0.191  0.84864    
## vaccine_doses_administered.l7 -9.148e-06  1.090e-05  -0.839  0.40186    
## mobility_mean.l7               1.080e-01  6.422e-02   1.682  0.09342 .  
## case_count_d1.l7              -6.782e-05  7.366e-05  -0.921  0.35786    
## tests_taken.l8                 3.555e-06  5.369e-06   0.662  0.50828    
## vaccine_doses_administered.l8  7.578e-06  8.784e-06   0.863  0.38887    
## mobility_mean.l8              -7.578e-02  5.521e-02  -1.373  0.17070    
## case_count_d1.l8               8.182e-05  6.268e-05   1.305  0.19258    
## const                          1.099e-01  6.585e-01   0.167  0.86752    
## sd1                            3.347e+00  1.224e+00   2.734  0.00656 ** 
## sd2                            3.273e+00  1.368e+00   2.394  0.01719 *  
## sd3                            2.966e+00  1.164e+00   2.548  0.01125 *  
## sd4                            1.012e+00  1.159e+00   0.873  0.38313    
## sd5                            6.313e+00  1.351e+00   4.673 4.18e-06 ***
## sd6                            1.882e+00  1.194e+00   1.576  0.11596    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.639 on 368 degrees of freedom
## Multiple R-Squared: 0.7627,  Adjusted R-squared: 0.7382 
## F-statistic: 31.12 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count_d1: 
## ============================================== 
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 7.603e-04  4.129e-03   0.184 0.853986    
## vaccine_doses_administered.l1  1.639e-02  6.724e-03   2.438 0.015253 *  
## mobility_mean.l1               2.283e+02  4.118e+01   5.544 5.66e-08 ***
## case_count_d1.l1              -6.820e-01  5.090e-02 -13.399  < 2e-16 ***
## tests_taken.l2                 8.266e-03  4.100e-03   2.016 0.044512 *  
## vaccine_doses_administered.l2 -1.004e-02  8.376e-03  -1.199 0.231464    
## mobility_mean.l2              -8.686e+01  4.993e+01  -1.740 0.082741 .  
## case_count_d1.l2              -7.203e-01  5.995e-02 -12.016  < 2e-16 ***
## tests_taken.l3                 1.212e-02  4.029e-03   3.007 0.002819 ** 
## vaccine_doses_administered.l3  1.222e-02  8.280e-03   1.475 0.141009    
## mobility_mean.l3              -6.250e+01  5.029e+01  -1.243 0.214734    
## case_count_d1.l3              -6.201e-01  6.769e-02  -9.161  < 2e-16 ***
## tests_taken.l4                -1.015e-03  4.000e-03  -0.254 0.799775    
## vaccine_doses_administered.l4 -1.050e-02  8.249e-03  -1.273 0.203874    
## mobility_mean.l4              -1.017e+02  5.016e+01  -2.028 0.043267 *  
## case_count_d1.l4              -4.910e-01  6.910e-02  -7.105 6.26e-12 ***
## tests_taken.l5                -4.848e-03  3.983e-03  -1.217 0.224273    
## vaccine_doses_administered.l5  4.646e-03  8.266e-03   0.562 0.574402    
## mobility_mean.l5               2.415e+01  4.997e+01   0.483 0.629223    
## case_count_d1.l5              -5.159e-01  6.768e-02  -7.623 2.13e-13 ***
## tests_taken.l6                -7.156e-03  4.030e-03  -1.776 0.076561 .  
## vaccine_doses_administered.l6  2.992e-03  8.311e-03   0.360 0.719009    
## mobility_mean.l6              -1.295e+01  4.992e+01  -0.259 0.795440    
## case_count_d1.l6              -2.573e-01  6.622e-02  -3.886 0.000121 ***
## tests_taken.l7                -1.077e-02  4.119e-03  -2.614 0.009319 ** 
## vaccine_doses_administered.l7 -1.647e-02  8.428e-03  -1.954 0.051507 .  
## mobility_mean.l7              -3.035e+01  4.966e+01  -0.611 0.541427    
## case_count_d1.l7              -4.390e-02  5.696e-02  -0.771 0.441401    
## tests_taken.l8                -3.422e-03  4.152e-03  -0.824 0.410326    
## vaccine_doses_administered.l8 -2.441e-03  6.792e-03  -0.359 0.719539    
## mobility_mean.l8               7.150e+01  4.269e+01   1.675 0.094801 .  
## case_count_d1.l8               9.050e-03  4.847e-02   0.187 0.851977    
## const                          1.059e+03  5.092e+02   2.081 0.038163 *  
## sd1                            3.761e+03  9.465e+02   3.974 8.52e-05 ***
## sd2                            2.966e+03  1.057e+03   2.805 0.005298 ** 
## sd3                            1.096e+03  9.001e+02   1.218 0.224020    
## sd4                            1.502e+03  8.966e+02   1.675 0.094833 .  
## sd5                            2.191e+03  1.045e+03   2.097 0.036660 *  
## sd6                           -2.380e+03  9.236e+02  -2.577 0.010352 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 2814 on 368 degrees of freedom
## Multiple R-Squared: 0.625,   Adjusted R-squared: 0.5863 
## F-statistic: 16.14 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                  1.260e+09                   16342922       -859.88
## vaccine_doses_administered   1.634e+07                  381104275      18710.29
## mobility_mean               -8.599e+02                      18710         13.24
## case_count_d1                1.674e+06                    2738784        503.48
##                            case_count_d1
## tests_taken                    1673507.5
## vaccine_doses_administered     2738783.9
## mobility_mean                      503.5
## case_count_d1                  7917357.8
## 
## Correlation matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                   1.000000                    0.02358     -0.006657
## vaccine_doses_administered    0.023584                    1.00000      0.263391
## mobility_mean                -0.006657                    0.26339      1.000000
## case_count_d1                 0.016755                    0.04986      0.049174
##                            case_count_d1
## tests_taken                      0.01675
## vaccine_doses_administered       0.04986
## mobility_mean                    0.04917
## case_count_d1                    1.00000

preds=predict(fit6a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(min(preds$fcst$case_count[,2]),12100))
lines(preds$fcst$case_count[,1],type = "l",col='blue')
lines(preds$fcst$case_count[,2],type = "l",col='blue',lty=2)
lines(preds$fcst$case_count[,3],type = "l",col='blue',lty=2)

short_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2) 
short_ASE_fit6a

## [1] 1289917

short_ASE_fit6a^.5

## [1] 1135.745

#7 Day RMSE of 1135.7
#Maybe try to look up rolling window version

long_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds$fcst$case_count[,1])^2) 
long_ASE_fit6a

## [1] 1247105

long_ASE_fit6a^.5

## [1] 1116.739

#21 Day RMSE of 1116.739 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE

Summarize VAR results

#Minimize Short 7 Day Forecast RMSE selects model fit6a (diff response with seasonality and lag of 8) - RMSE of 1135.75
(short_ASE_fit1a)^.5

## [1] 1763.689

(short_ASE_fit2a)^.5

## [1] 2066.276

(short_ASE_fit2b)^.5

## [1] 1595.717

(short_ASE_fit3a)^.5

## [1] 1278.838

(short_ASE_fit4a)^.5

## [1] 1143.21

(short_ASE_fit5a)^.5

## [1] 1300.18

(short_ASE_fit6a)^.5

## [1] 1135.745

min(short_ASE_fit1a,short_ASE_fit2a,short_ASE_fit2b,short_ASE_fit3a,short_ASE_fit4a,short_ASE_fit5a,short_ASE_fit6a)^.5

## [1] 1135.745

#Minimize Long 21 Day Forecast RMSE selects model fit3a (diff all data without seasonality lag of 8) - RMSE of 974.29
(long_ASE_fit1a)^.5

## [1] 1326.601

(long_ASE_fit2a)^.5

## [1] 1522.145

(long_ASE_fit2b)^.5

## [1] 2635.849

(long_ASE_fit3a)^.5

## [1] 974.2925

(long_ASE_fit4a)^.5

## [1] 1185.561

(long_ASE_fit5a)^.5

## [1] 994.3586

(long_ASE_fit6a)^.5

## [1] 1116.739

min(long_ASE_fit1a,long_ASE_fit2a,long_ASE_fit2b,long_ASE_fit3a,long_ASE_fit4a,long_ASE_fit5a,long_ASE_fit6a)^.5

## [1] 974.2925

#Minimize Short 7 Day Forecast AIC selects model fit6a (diff response with seasonality and lag of 8) - AIC of 7659
AIC(fit1a$varresult$case_count)

## [1] 7731.964

AIC(fit2a$varresult$case_count)

## [1] 7692.989

AIC(fit2b$varresult$case_count)

## [1] 7909.099

AIC(fit3a$varresult$case_count)

## [1] 7731.493

AIC(fit4a$varresult$case_count)

## [1] 7692.788

AIC(fit5a$varresult$case_count)

## [1] 7697.388

AIC(fit6a$varresult$case_count)

## [1] 7659.038

#Minimize Short 7 Day Forecast BIC selects model fit6a (diff response with seasonality and lag of 8) - BIC of 7819
BIC(fit1a$varresult$case_count)

## [1] 7868.347

BIC(fit2a$varresult$case_count)

## [1] 7853.439

BIC(fit2b$varresult$case_count)

## [1] 7973.513

BIC(fit3a$varresult$case_count)

## [1] 7851.831

BIC(fit4a$varresult$case_count)

## [1] 7837.194

BIC(fit5a$varresult$case_count)

## [1] 7833.688

BIC(fit6a$varresult$case_count)

## [1] 7819.39

Create MLP models

###MLP with reduced original data

#Create train and whole ts set
covid_reduced_train=covid_reduced[1:(dim(covid_reduced)[1]-21),]

covid_reduced_train$case_count <- ts(covid_reduced_train$case_count, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$tests_taken <- ts(covid_reduced_train$tests_taken, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$vaccine_doses_administered <- ts(covid_reduced_train$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$mobility_mean <- ts(covid_reduced_train$mobility_mean, start = decimal_date(as.Date("2020-09-14")), frequency = 365)

covid_reduced_ts=covid_reduced

covid_reduced_ts$case_count <- ts(covid_reduced_ts$case_count, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$tests_taken <- ts(covid_reduced_ts$tests_taken, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$vaccine_doses_administered <- ts(covid_reduced_ts$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$mobility_mean <- ts(covid_reduced_ts$mobility_mean, start = decimal_date(as.Date("2020-09-14")), frequency = 365)

#Fit model and forecast
set.seed(2)
fit_mlp1 = mlp(y = covid_reduced_train$case_count,xreg = covid_reduced_train[,c(1,3,4)],hd.auto.type = 'cv',reps =  30,comb = 'median',allow.det.season = T)
fit_mlp1

## MLP fit with 1 hidden node and 30 repetitions.
## Series modelled in differences: D1.
## Univariate lags: (7,28,49,86,345)
## 2 regressors included.
## - Regressor 1 lags: (9,16,114)
## - Regressor 2 lags: (118)
## Forecast combined using the median operator.
## MSE: 17691565.0178.

plot(fit_mlp1)

short_f_mlp1 = forecast(fit_mlp1, h = 7, xreg = covid_reduced_ts[,c(1,3,4)])
plot(short_f_mlp1,xlim=c(2021.7,2022))

plot(seq(1,7),tail(covid_reduced_ts$case_count,21)[1:7],type = "l",ylim=c(-4800,12000)) 
lines(seq(1,7),short_f_mlp1$mean, col = "blue",type= 'l')

short_ASE_fit_mlp1 = mean((tail(covid_reduced_ts$case_count,21)[1:7]-short_f_mlp1$mean)^2) 
short_ASE_fit_mlp1^.5

## [1] 3698.237

#RMSE of 3698

long_f_mlp1 = forecast(fit_mlp1, h = 21, xreg = covid_reduced_ts[,c(1,3,4)],level=c(95))

plot(long_f_mlp1,xlim=c(2021.7,2022))

plot(long_f_mlp1$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
    lines(long_f_mlp1$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid_reduced_ts$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),tail(covid_reduced_ts$case_count,21),type = "l",ylim=c(-6500,12000)) 
lines(seq(1,21),long_f_mlp1$mean, col = "blue",type= 'l')

long_ASE_fit_mlp1 = mean((tail(covid_reduced_ts$case_count,21)-long_f_mlp1$mean)^2) 
long_ASE_fit_mlp1^.5

## [1] 4795.097

#RMSE 4795

###Use differenced repsonse set

#Create train and whole ts set
covid_reduced_cases_d1_train=covid_reduced_cases_d1[1:(dim(covid_reduced_cases_d1)[1]-21),]

covid_reduced_cases_d1_train$case_count_d1 <- ts(covid_reduced_cases_d1_train$case_count_d1, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$tests_taken <- ts(covid_reduced_cases_d1_train$tests_taken, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$vaccine_doses_administered <- ts(covid_reduced_cases_d1_train$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$mobility_mean <- ts(covid_reduced_cases_d1_train$mobility_mean, start = decimal_date(as.Date("2020-09-15")), frequency = 365)

covid_reduced_cases_d1_ts=covid_reduced_cases_d1

covid_reduced_cases_d1_ts$case_count_d1 <- ts(covid_reduced_cases_d1_ts$case_count_d1, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$tests_taken <- ts(covid_reduced_cases_d1_ts$tests_taken, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$vaccine_doses_administered <- ts(covid_reduced_cases_d1_ts$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$mobility_mean <- ts(covid_reduced_cases_d1_ts$mobility_mean, start = decimal_date(as.Date("2020-09-15")), frequency = 365)

#Fit model and forecast
set.seed(2)
fit_mlp2 = mlp(y = covid_reduced_cases_d1_train$case_count_d1,xreg = covid_reduced_cases_d1_train[,c(1,2,3)],hd.auto.type = 'cv',reps =  30,comb = 'median',allow.det.season = T)
fit_mlp2

## MLP fit with 1 hidden node and 30 repetitions.
## Univariate lags: (7,28,49,86,345)
## 2 regressors included.
## - Regressor 1 lags: (9,16,114)
## - Regressor 2 lags: (118)
## Forecast combined using the median operator.
## MSE: 17691565.0178.

plot(fit_mlp2)

short_f_mlp2 = forecast(fit_mlp2, h = 7, xreg = covid_reduced_cases_d1_ts[,c(1,2,3)])
plot(short_f_mlp2,xlim=c(2021.7,2022))

plot(seq(1,7),tail(covid_reduced_cases_d1_ts$case_count_d1,21)[1:7],type = "l",ylim=c(-4800,12000)) 
lines(seq(1,7),short_f_mlp2$mean, col = "blue",type= 'l')

short_ASE_fit_mlp2 = mean((tail(covid_reduced_cases_d1_ts$case_count_d1,21)[1:7]-short_f_mlp2$mean)^2) 
short_ASE_fit_mlp2^.5

## [1] 2760.336

#RMSE of 2760

long_f_mlp2 = forecast(fit_mlp2, h = 21, xreg = covid_reduced_cases_d1_ts[,c(1,2,3)])
plot(long_f_mlp2,xlim=c(2021.7,2022))

plot(seq(1,21),tail(covid_reduced_cases_d1_ts$case_count_d1,21),type = "l",ylim=c(-6500,12000)) 
lines(seq(1,21),long_f_mlp2$mean, col = "blue",type= 'l')

long_ASE_fit_mlp2 = mean((tail(covid_reduced_cases_d1_ts$case_count_d1,21)-long_f_mlp2$mean)^2) 
long_ASE_fit_mlp2^.5

## [1] 5787.929

#RMSE 5788

#Selected MLP Model1
covidData = ts(covid$case_count[1:395])
covidXX = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]), park_mobility= ts(covid$parks_percent_change_from_baseline[1:395]))
covidXX_full = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered), park_mobility= ts(covid$parks_percent_change_from_baseline))
set.seed(2)
fitCOVIDXX = mlp(covidData,xreg = covidXX)
fcstCOVIDXX= forecast(fitCOVIDXX,h=21,xreg = covidXX_full)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
    lines(seq(1,21),fcstCOVIDXX$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX$mean,col = "red")

ASE_DEEP_SHORT_XX = mean((tail(covid$case_count,21)[1:7] - fcstCOVIDXX$mean[1:7])^2)
ASE_DEEP_SHORT_XX

## [1] 907508.8

RMSE_DEEP_SHORT_XX = sqrt(ASE_DEEP_SHORT_XX)
RMSE_DEEP_SHORT_XX

## [1] 952.6326

ASE_DEEP_LONG_XX = mean((tail(covid$case_count,21) - fcstCOVIDXX$mean)^2)
ASE_DEEP_LONG_XX

## [1] 1589160

RMSE_DEEP_LONG_XX = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX

## [1] 1260.619

#Selected MLP Model2
covidData = ts(covid$case_count[1:395])
covidXX2 = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]))
covidXX_full2 = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered))
set.seed(2)
fitCOVIDXX2 = mlp(covidData,xreg = covidXX2)
fcstCOVIDXX2= forecast(fitCOVIDXX2,h=21,xreg = covidXX_full2)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
    lines(seq(1,21),fcstCOVIDXX2$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX2$mean,col = "red")

ASE_DEEP_SHORT_XX2 = mean((tail(covid$case_count,21)[1:7] - fcstCOVIDXX2$mean[1:7])^2)
ASE_DEEP_SHORT_XX2

## [1] 2971978

RMSE_DEEP_SHORT_XX2 = sqrt(ASE_DEEP_SHORT_XX2)
RMSE_DEEP_SHORT_XX2

## [1] 1723.943

ASE_DEEP_LONG_XX2 = mean((tail(covid$case_count,21) - fcstCOVIDXX2$mean)^2)
ASE_DEEP_LONG_XX2

## [1] 5645679

RMSE_DEEP_LONG_XX2 = sqrt(ASE_DEEP_LONG_XX2)
RMSE_DEEP_LONG_XX2

## [1] 2376.064

MLP RMSE Summary

(short_ASE_fit_mlp1)^.5

## [1] 3698.237

(short_ASE_fit_mlp2)^.5

## [1] 2760.336

(long_ASE_fit_mlp1)^.5

## [1] 4795.097

(long_ASE_fit_mlp2)^.5

## [1] 5787.929

RMSE_DEEP_SHORT_XX #Selected Model For Ensemble

## [1] 952.6326

RMSE_DEEP_LONG_XX #Selected Model For Ensemble

## [1] 1260.619

RMSE_DEEP_SHORT_XX2

## [1] 1723.943

RMSE_DEEP_LONG_XX2

## [1] 2376.064

Selected MLP/VAR Models and Ensemble Model

#Selected VAR Model
#Fit based on AIC
fit6a=VAR(covid_reduced_cases_d1,p=8,type="const",season = 7)
summary(fit6a)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1 
## Deterministic variables: const 
## Sample size: 407 
## Log Likelihood: -14255.72 
## Roots of the characteristic polynomial:
## 0.9841 0.9841 0.9737 0.9737 0.948 0.948 0.9274 0.9033 0.9033 0.8907 0.8907 0.849 0.849 0.795 0.795 0.7874 0.7874 0.767 0.767 0.7257 0.7257 0.7025 0.7025 0.6991 0.6767 0.6767 0.6408 0.6408 0.5814 0.5814 0.3624 0.2511
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const", season = 7L)
## 
## 
## Estimation results for equation tests_taken: 
## ============================================ 
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 8.333e-02  5.208e-02   1.600 0.110470    
## vaccine_doses_administered.l1  9.619e-02  8.482e-02   1.134 0.257499    
## mobility_mean.l1               1.313e+02  5.195e+02   0.253 0.800632    
## case_count_d1.l1               1.216e+00  6.421e-01   1.894 0.058977 .  
## tests_taken.l2                 5.396e-02  5.172e-02   1.043 0.297555    
## vaccine_doses_administered.l2 -8.942e-02  1.057e-01  -0.846 0.397978    
## mobility_mean.l2               4.686e+02  6.298e+02   0.744 0.457374    
## case_count_d1.l2               1.477e+00  7.562e-01   1.953 0.051593 .  
## tests_taken.l3                 4.349e-03  5.083e-02   0.086 0.931857    
## vaccine_doses_administered.l3  7.423e-02  1.045e-01   0.711 0.477782    
## mobility_mean.l3               1.640e+02  6.345e+02   0.259 0.796142    
## case_count_d1.l3               2.053e+00  8.540e-01   2.404 0.016697 *  
## tests_taken.l4                 2.094e-01  5.046e-02   4.150 4.14e-05 ***
## vaccine_doses_administered.l4  3.472e-02  1.041e-01   0.334 0.738887    
## mobility_mean.l4              -1.469e+01  6.328e+02  -0.023 0.981492    
## case_count_d1.l4               6.219e-01  8.717e-01   0.713 0.476021    
## tests_taken.l5                 1.639e-01  5.025e-02   3.262 0.001210 ** 
## vaccine_doses_administered.l5  1.988e-02  1.043e-01   0.191 0.848917    
## mobility_mean.l5              -1.095e+02  6.305e+02  -0.174 0.862259    
## case_count_d1.l5               2.469e+00  8.539e-01   2.892 0.004059 ** 
## tests_taken.l6                 1.912e-01  5.083e-02   3.762 0.000196 ***
## vaccine_doses_administered.l6 -1.781e-01  1.048e-01  -1.699 0.090247 .  
## mobility_mean.l6              -3.290e+02  6.297e+02  -0.522 0.601652    
## case_count_d1.l6               1.760e+00  8.354e-01   2.107 0.035822 *  
## tests_taken.l7                 1.543e-01  5.197e-02   2.969 0.003187 ** 
## vaccine_doses_administered.l7  8.960e-02  1.063e-01   0.843 0.399956    
## mobility_mean.l7              -9.509e+01  6.265e+02  -0.152 0.879442    
## case_count_d1.l7               8.859e-01  7.186e-01   1.233 0.218442    
## tests_taken.l8                 3.202e-02  5.237e-02   0.611 0.541396    
## vaccine_doses_administered.l8 -6.130e-02  8.569e-02  -0.715 0.474788    
## mobility_mean.l8              -1.771e+02  5.386e+02  -0.329 0.742485    
## case_count_d1.l8               3.954e-01  6.114e-01   0.647 0.518249    
## const                          1.195e+04  6.424e+03   1.860 0.063734 .  
## sd1                           -8.726e+03  1.194e+04  -0.731 0.465412    
## sd2                            1.527e+03  1.334e+04   0.114 0.908911    
## sd3                            6.752e+03  1.136e+04   0.595 0.552464    
## sd4                            1.006e+04  1.131e+04   0.889 0.374573    
## sd5                           -8.065e+03  1.318e+04  -0.612 0.540949    
## sd6                            1.595e+03  1.165e+04   0.137 0.891177    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 35500 on 368 degrees of freedom
## Multiple R-Squared: 0.4696,  Adjusted R-squared: 0.4149 
## F-statistic: 8.575 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation vaccine_doses_administered: 
## =========================================================== 
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                -2.152e-02  2.864e-02  -0.751  0.45291    
## vaccine_doses_administered.l1  8.631e-01  4.665e-02  18.503  < 2e-16 ***
## mobility_mean.l1               1.663e+02  2.857e+02   0.582  0.56088    
## case_count_d1.l1              -5.244e-01  3.531e-01  -1.485  0.13840    
## tests_taken.l2                 1.237e-02  2.845e-02   0.435  0.66399    
## vaccine_doses_administered.l2 -1.067e-01  5.811e-02  -1.836  0.06719 .  
## mobility_mean.l2               6.954e+02  3.464e+02   2.007  0.04543 *  
## case_count_d1.l2              -3.295e-01  4.159e-01  -0.792  0.42869    
## tests_taken.l3                -1.810e-03  2.796e-02  -0.065  0.94841    
## vaccine_doses_administered.l3 -6.832e-02  5.745e-02  -1.189  0.23510    
## mobility_mean.l3              -3.349e+01  3.489e+02  -0.096  0.92360    
## case_count_d1.l3              -3.185e-01  4.696e-01  -0.678  0.49810    
## tests_taken.l4                -2.497e-02  2.775e-02  -0.900  0.36874    
## vaccine_doses_administered.l4  1.368e-01  5.723e-02   2.389  0.01738 *  
## mobility_mean.l4              -3.683e+00  3.480e+02  -0.011  0.99156    
## case_count_d1.l4              -2.335e-01  4.794e-01  -0.487  0.62652    
## tests_taken.l5                 1.212e-02  2.763e-02   0.439  0.66117    
## vaccine_doses_administered.l5 -1.284e-01  5.735e-02  -2.239  0.02573 *  
## mobility_mean.l5              -3.370e+02  3.467e+02  -0.972  0.33166    
## case_count_d1.l5               2.113e-02  4.696e-01   0.045  0.96414    
## tests_taken.l6                -1.230e-02  2.796e-02  -0.440  0.66015    
## vaccine_doses_administered.l6  1.904e-01  5.766e-02   3.302  0.00105 ** 
## mobility_mean.l6              -3.515e+02  3.463e+02  -1.015  0.31081    
## case_count_d1.l6              -5.690e-01  4.595e-01  -1.239  0.21632    
## tests_taken.l7                 2.763e-02  2.858e-02   0.967  0.33429    
## vaccine_doses_administered.l7  5.656e-01  5.847e-02   9.672  < 2e-16 ***
## mobility_mean.l7              -2.586e+02  3.445e+02  -0.751  0.45333    
## case_count_d1.l7              -2.550e-02  3.952e-01  -0.065  0.94859    
## tests_taken.l8                -6.493e-03  2.880e-02  -0.225  0.82178    
## vaccine_doses_administered.l8 -4.770e-01  4.713e-02 -10.121  < 2e-16 ***
## mobility_mean.l8              -1.991e+02  2.962e+02  -0.672  0.50181    
## case_count_d1.l8               1.754e-01  3.363e-01   0.522  0.60227    
## const                          4.138e+02  3.533e+03   0.117  0.90683    
## sd1                           -1.872e+04  6.567e+03  -2.851  0.00460 ** 
## sd2                           -1.070e+04  7.337e+03  -1.458  0.14570    
## sd3                           -8.764e+03  6.245e+03  -1.403  0.16134    
## sd4                           -9.777e+03  6.220e+03  -1.572  0.11685    
## sd5                           -2.127e+04  7.248e+03  -2.934  0.00356 ** 
## sd6                           -2.693e+04  6.408e+03  -4.203 3.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 19520 on 368 degrees of freedom
## Multiple R-Squared: 0.9445,  Adjusted R-squared: 0.9387 
## F-statistic: 164.7 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation mobility_mean: 
## ============================================== 
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 1.571e-07  5.339e-06   0.029  0.97653    
## vaccine_doses_administered.l1  6.011e-06  8.695e-06   0.691  0.48976    
## mobility_mean.l1               6.730e-01  5.325e-02  12.638  < 2e-16 ***
## case_count_d1.l1              -1.158e-04  6.582e-05  -1.760  0.07922 .  
## tests_taken.l2                -4.497e-06  5.302e-06  -0.848  0.39692    
## vaccine_doses_administered.l2 -1.146e-05  1.083e-05  -1.058  0.29067    
## mobility_mean.l2               1.036e-01  6.456e-02   1.604  0.10960    
## case_count_d1.l2              -1.201e-04  7.752e-05  -1.550  0.12203    
## tests_taken.l3                 3.565e-06  5.211e-06   0.684  0.49428    
## vaccine_doses_administered.l3  7.944e-06  1.071e-05   0.742  0.45864    
## mobility_mean.l3              -1.292e-02  6.504e-02  -0.199  0.84261    
## case_count_d1.l3              -1.874e-04  8.754e-05  -2.141  0.03293 *  
## tests_taken.l4                -1.210e-05  5.173e-06  -2.339  0.01989 *  
## vaccine_doses_administered.l4 -9.375e-06  1.067e-05  -0.879  0.38011    
## mobility_mean.l4               7.083e-02  6.487e-02   1.092  0.27555    
## case_count_d1.l4              -1.581e-04  8.936e-05  -1.770  0.07759 .  
## tests_taken.l5                -5.268e-06  5.151e-06  -1.023  0.30710    
## vaccine_doses_administered.l5  1.754e-06  1.069e-05   0.164  0.86974    
## mobility_mean.l5              -4.643e-02  6.463e-02  -0.718  0.47292    
## case_count_d1.l5              -1.032e-04  8.753e-05  -1.179  0.23915    
## tests_taken.l6                 7.607e-07  5.211e-06   0.146  0.88402    
## vaccine_doses_administered.l6  7.434e-06  1.075e-05   0.692  0.48960    
## mobility_mean.l6               6.931e-02  6.455e-02   1.074  0.28368    
## case_count_d1.l6              -1.032e-04  8.564e-05  -1.205  0.22885    
## tests_taken.l7                 1.017e-06  5.327e-06   0.191  0.84864    
## vaccine_doses_administered.l7 -9.148e-06  1.090e-05  -0.839  0.40186    
## mobility_mean.l7               1.080e-01  6.422e-02   1.682  0.09342 .  
## case_count_d1.l7              -6.782e-05  7.366e-05  -0.921  0.35786    
## tests_taken.l8                 3.555e-06  5.369e-06   0.662  0.50828    
## vaccine_doses_administered.l8  7.578e-06  8.784e-06   0.863  0.38887    
## mobility_mean.l8              -7.578e-02  5.521e-02  -1.373  0.17070    
## case_count_d1.l8               8.182e-05  6.268e-05   1.305  0.19258    
## const                          1.099e-01  6.585e-01   0.167  0.86752    
## sd1                            3.347e+00  1.224e+00   2.734  0.00656 ** 
## sd2                            3.273e+00  1.368e+00   2.394  0.01719 *  
## sd3                            2.966e+00  1.164e+00   2.548  0.01125 *  
## sd4                            1.012e+00  1.159e+00   0.873  0.38313    
## sd5                            6.313e+00  1.351e+00   4.673 4.18e-06 ***
## sd6                            1.882e+00  1.194e+00   1.576  0.11596    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 3.639 on 368 degrees of freedom
## Multiple R-Squared: 0.7627,  Adjusted R-squared: 0.7382 
## F-statistic: 31.12 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## Estimation results for equation case_count_d1: 
## ============================================== 
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 
## 
##                                 Estimate Std. Error t value Pr(>|t|)    
## tests_taken.l1                 7.603e-04  4.129e-03   0.184 0.853986    
## vaccine_doses_administered.l1  1.639e-02  6.724e-03   2.438 0.015253 *  
## mobility_mean.l1               2.283e+02  4.118e+01   5.544 5.66e-08 ***
## case_count_d1.l1              -6.820e-01  5.090e-02 -13.399  < 2e-16 ***
## tests_taken.l2                 8.266e-03  4.100e-03   2.016 0.044512 *  
## vaccine_doses_administered.l2 -1.004e-02  8.376e-03  -1.199 0.231464    
## mobility_mean.l2              -8.686e+01  4.993e+01  -1.740 0.082741 .  
## case_count_d1.l2              -7.203e-01  5.995e-02 -12.016  < 2e-16 ***
## tests_taken.l3                 1.212e-02  4.029e-03   3.007 0.002819 ** 
## vaccine_doses_administered.l3  1.222e-02  8.280e-03   1.475 0.141009    
## mobility_mean.l3              -6.250e+01  5.029e+01  -1.243 0.214734    
## case_count_d1.l3              -6.201e-01  6.769e-02  -9.161  < 2e-16 ***
## tests_taken.l4                -1.015e-03  4.000e-03  -0.254 0.799775    
## vaccine_doses_administered.l4 -1.050e-02  8.249e-03  -1.273 0.203874    
## mobility_mean.l4              -1.017e+02  5.016e+01  -2.028 0.043267 *  
## case_count_d1.l4              -4.910e-01  6.910e-02  -7.105 6.26e-12 ***
## tests_taken.l5                -4.848e-03  3.983e-03  -1.217 0.224273    
## vaccine_doses_administered.l5  4.646e-03  8.266e-03   0.562 0.574402    
## mobility_mean.l5               2.415e+01  4.997e+01   0.483 0.629223    
## case_count_d1.l5              -5.159e-01  6.768e-02  -7.623 2.13e-13 ***
## tests_taken.l6                -7.156e-03  4.030e-03  -1.776 0.076561 .  
## vaccine_doses_administered.l6  2.992e-03  8.311e-03   0.360 0.719009    
## mobility_mean.l6              -1.295e+01  4.992e+01  -0.259 0.795440    
## case_count_d1.l6              -2.573e-01  6.622e-02  -3.886 0.000121 ***
## tests_taken.l7                -1.077e-02  4.119e-03  -2.614 0.009319 ** 
## vaccine_doses_administered.l7 -1.647e-02  8.428e-03  -1.954 0.051507 .  
## mobility_mean.l7              -3.035e+01  4.966e+01  -0.611 0.541427    
## case_count_d1.l7              -4.390e-02  5.696e-02  -0.771 0.441401    
## tests_taken.l8                -3.422e-03  4.152e-03  -0.824 0.410326    
## vaccine_doses_administered.l8 -2.441e-03  6.792e-03  -0.359 0.719539    
## mobility_mean.l8               7.150e+01  4.269e+01   1.675 0.094801 .  
## case_count_d1.l8               9.050e-03  4.847e-02   0.187 0.851977    
## const                          1.059e+03  5.092e+02   2.081 0.038163 *  
## sd1                            3.761e+03  9.465e+02   3.974 8.52e-05 ***
## sd2                            2.966e+03  1.057e+03   2.805 0.005298 ** 
## sd3                            1.096e+03  9.001e+02   1.218 0.224020    
## sd4                            1.502e+03  8.966e+02   1.675 0.094833 .  
## sd5                            2.191e+03  1.045e+03   2.097 0.036660 *  
## sd6                           -2.380e+03  9.236e+02  -2.577 0.010352 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 2814 on 368 degrees of freedom
## Multiple R-Squared: 0.625,   Adjusted R-squared: 0.5863 
## F-statistic: 16.14 on 38 and 368 DF,  p-value: < 2.2e-16 
## 
## 
## 
## Covariance matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                  1.260e+09                   16342922       -859.88
## vaccine_doses_administered   1.634e+07                  381104275      18710.29
## mobility_mean               -8.599e+02                      18710         13.24
## case_count_d1                1.674e+06                    2738784        503.48
##                            case_count_d1
## tests_taken                    1673507.5
## vaccine_doses_administered     2738783.9
## mobility_mean                      503.5
## case_count_d1                  7917357.8
## 
## Correlation matrix of residuals:
##                            tests_taken vaccine_doses_administered mobility_mean
## tests_taken                   1.000000                    0.02358     -0.006657
## vaccine_doses_administered    0.023584                    1.00000      0.263391
## mobility_mean                -0.006657                    0.26339      1.000000
## case_count_d1                 0.016755                    0.04986      0.049174
##                            case_count_d1
## tests_taken                      0.01675
## vaccine_doses_administered       0.04986
## mobility_mean                    0.04917
## case_count_d1                    1.00000

preds_6a=predict(fit6a,n.ahead=21)
par(mfrow=c(1,1))

#Fan charts
fanchart(preds_6a, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds_6a$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(min(preds_6a$fcst$case_count[,2]),12100))
lines(preds_6a$fcst$case_count[,1],type = "l",col='blue')
lines(preds_6a$fcst$case_count[,2],type = "l",col='blue',lty=2)
lines(preds_6a$fcst$case_count[,3],type = "l",col='blue',lty=2)

short_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds_6a$fcst$case_count[1:7,1])^2) 
short_ASE_fit6a

## [1] 1289917

short_ASE_fit6a^.5

## [1] 1135.745

#7 Day RMSE of 1135.7
#Maybe try to look up rolling window version

long_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds_6a$fcst$case_count[,1])^2) 
long_ASE_fit6a

## [1] 1247105

long_ASE_fit6a^.5

## [1] 1116.739

#21 Day RMSE of 1116.739 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE

#Selected MLP Model1
covidData = ts(covid$case_count[1:395])
covidXX = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]), park_mobility= ts(covid$parks_percent_change_from_baseline[1:395]))
covidXX_full = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered), park_mobility= ts(covid$parks_percent_change_from_baseline))
set.seed(2)
fitCOVIDXX = mlp(covidData,xreg = covidXX)
fcstCOVIDXX= forecast(fitCOVIDXX,h=21,xreg = covidXX_full)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
    lines(seq(1,21),fcstCOVIDXX$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX$mean,col = "red")

ASE_DEEP_LONG_XX = mean((tail(covid$case_count,21) - fcstCOVIDXX$mean)^2)
ASE_DEEP_LONG_XX

## [1] 1589160

RMSE_DEEP_LONG_XX = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX

## [1] 1260.619

#Selected MLP Model2
covidData = ts(covid$case_count[1:395])
covidXX2 = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]))
covidXX_full2 = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered))
set.seed(2)
fitCOVIDXX2 = mlp(covidData,xreg = covidXX2)
fcstCOVIDXX2= forecast(fitCOVIDXX2,h=21,xreg = covidXX_full2)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
    lines(seq(1,21),fcstCOVIDXX2$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX2$mean,col = "red")

ASE_DEEP_LONG_XX2 = mean((tail(covid$case_count,21) - fcstCOVIDXX2$mean)^2)
ASE_DEEP_LONG_XX2

## [1] 5645679

RMSE_DEEP_LONG_XX2 = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX2

## [1] 1260.619

#Ensemble forecast
adj_preds2=preds_6a$fcst$case_count_d1[,1]+tail(covid$case_count,22)[1:21]
plot(adj_preds2,type='l',ylim=c(-10000,10000))
lines(tail(covid$case_count,21),col='blue')

adj_ASE_6a = mean((tail(covid$case_count,21)-adj_preds2)^2) 
adj_ASE_6a^.5

## [1] 1116.739

ensemble_preds=(adj_preds2+fcstCOVIDXX$mean)/2
plot(tail(covid$case_count,21),type='l',ylim=c(-10000,10000))
lines(seq(1,21),tail(ensemble_preds,21),col='blue')

ensemble_ASE = mean((tail(covid$case_count,21)[1:7]-ensemble_preds[1:7])^2) 
ensemble_ASE^.5

## [1] 903.0232

ensemble_ASE = mean((tail(covid$case_count,21)-ensemble_preds)^2) 
ensemble_ASE^.5

## [1] 1031.55

#Final comparison plot
plot(tail(covid$case_count,21),type='l',ylim=c(0,7000),lwd=4)
lines(adj_preds2,type = "l",col='grey')
lines(seq(1,21),fcstCOVIDXX$mean,col = "grey")
lines(seq(1,21),tail(ensemble_preds,21),col='blue',lwd=2,lty=2)

#Final comparison plot
plot(tail(covid$case_count,100),type='l',ylim=c(0,30000),lwd=2)
lines(seq(80,100),adj_preds2,type = "l",col='dark grey')
lines(seq(80,100),fcstCOVIDXX$mean,col = "dark grey")
lines(seq(80,100),tail(ensemble_preds,21),col='blue',lwd=2,lty=2)